Methods and apparatus for compactly describing lifted low-density parity-check (ldpc) codes

ABSTRACT

Certain aspects of the present disclosure generally relate to techniques for compactly describing lifted low-density parity-check (LDPC) codes. A method by a transmitting device generally includes selecting a first lifting size value and a first set of lifting values; generating a first lifted LDPC code by applying the first set of lifting values to interconnect edges in copies of a parity check matrix (PCM) having a first number of variable nodes and a second number of check nodes; determining a second set of lifting values for generating a second lifted LDPC code for a second lifting size value based on the first lifted PCM and the first set of lifting values; encoding a set of information bits based the first lifted LDPC code or the second lifted LDPC code to produce a code word; and transmitting the code word.

CROSS-REFERENCE TO RELATED APPLICATIONS & PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.16/655,850, filed Oct. 17, 2019 (163764U1C1), which is a continuation ofU.S. patent application Ser. No. 15/622,019, filed Jun. 13, 2017(163764U1), which claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/349,784, filed Jun. 14, 2016 (163764P1), andU.S. Provisional Patent Application Ser. No. 62/374,514 (164403P1),filed Aug. 12, 2016, all of which are herein incorporated by referencein their entirety for all applicable purposes.

TECHNICAL FIELD

Certain aspects of the technology discussed below generally relate towireless communications, including detecting and/or correcting errors inbinary data and, more particularly, to methods and apparatus forcompactly describing lifted low-density parity-check (LDPC) codes.

INTRODUCTION

Wireless communication systems are widely deployed to provide varioustypes of communication content such as voice, video, data, message,broadcasts, and so on. These systems may employ multiple-accesstechnologies capable of supporting communication with multiple users bysharing available system resources (e.g., bandwidth and transmit power).Examples of such multiple-access systems include code division multipleaccess (CDMA) systems, time division multiple access (TDMA) systems,time division synchronous CDMA (TD-SCDMA) systems, frequency divisionmultiple access (FDMA) systems, single-carrier FDMA (SC-FDMA) systems,orthogonal FDMA (OFDMA), 3rd Generation Partnership Project (3GPP) longterm evolution (LTE) systems, and LTE Advanced (LTE-A) systems.

Multiple access technologies have been adopted in varioustelecommunication standards to provide a common protocol that enablesdifferent wireless devices to communicate on a municipal, national,regional, and even global level. An example of an emergingtelecommunication standard is new radio (NR), for example, 5G radioaccess. NR is a set of enhancements to the LTE mobile standardpromulgated by 3GPP. It is designed to better support mobile broadbandInternet access by improving spectral efficiency, lowering costs,improving services, making use of new spectrum, and better integratingwith other open standards using OFDMA with a cyclic prefix (CP) on thedownlink (DL) and on the uplink (UL) as well as support beamforming,multiple-input multiple-output (MIMO) antenna technology, and carrieraggregation.

Generally, a wireless multiple-access communication system cansimultaneously support communication for multiple wireless nodes. Eachnode communicates with one or more base stations (BSs) via transmissionson forward and reverse links. The forward link (or downlink) refers to acommunication link from BSs to nodes, and a reverse link (or uplink)refers to a communication link from nodes to base stations.Communication links may be established via a single-input single-output,multiple-input single-output, or a MIMO system.

In some examples, a wireless multiple-access communication system mayinclude a number of BSs, each simultaneously supporting communicationfor multiple communication devices, otherwise known as user equipment(UEs). In an LTE or LTE-A network, a set of one or more BSs may definean e NodeB (eNB). In other examples (e.g., in a next generation, NR, or5G network), a wireless multiple access communication system may includea number of distributed units (DUs) (e.g., edge units (EUs), edge nodes(ENs), radio heads (RHs), smart radio heads (SRHs), transmissionreception points (TRPs), etc.) in communication with a number of centralunits (CUs) (e.g., central nodes (CNs), access node controllers (ANCs),etc.), where a set of one or more DUs, in communication with a CU, maydefine an access node (e.g., a BS, a NR BS, a 5G BS, a NB, an eNB, NRNB, a 5G NB, an access point (AP),), a network node, a gNB, a TRP,etc.). A BS, AN, or DU may communicate with a UE or a set of UEs ondownlink channels (e.g., for transmissions from a BS or to a UE) anduplink channels (e.g., for transmissions from a UE to a BS, AN, or DU).

Binary values (e.g., ones and zeros), are used to represent andcommunicate various types of information, such as video, audio,statistical information, etc. Unfortunately, during storage,transmission, and/or processing of binary data, errors may beunintentionally introduced; for example, a “1” may be changed to a “0”or vice versa.

Generally, in the case of data transmission, a receiver observes eachreceived bit in the presence of noise or distortion and only anindication of the bit's value is obtained. Under these circumstances,the observed values are interpreted as a source of “soft” bits. A softbit indicates a preferred estimate of the bit's value (e.g., a 1 or a 0)together with some indication of the reliability of that estimate. Whilethe number of errors may be relatively low, even a small number oferrors or level of distortion can result in the data being unusable or,in the case of transmission errors, may necessitate re-transmission ofthe data. In order to provide a mechanism to check for errors and, insome cases, to correct errors, binary data can be coded to introducecarefully designed redundancy. Coding of a unit of data produces what iscommonly referred to as a codeword. Because of its redundancy, acodeword will often include more bits than the input unit of data fromwhich the codeword was produced.

Redundant bits are added by an encoder to the transmitted bitstream tocreate a codeword. When signals arising from transmitted codewords arereceived or processed, the redundant information included in thecodeword as observed in the signal can be used to identify and/orcorrect errors in or remove distortion from the received signal torecover the original data unit. Such error checking and/or correctingcan be implemented as part of a decoding process. In the absence oferrors, or in the case of correctable errors or distortion, decoding canbe used to recover from the source data being processed, the originaldata unit that was encoded. In the case of unrecoverable errors, thedecoding process may produce some indication that the original datacannot be fully recovered. Such indications of decoding failure initiateretransmission of the data. As the use of fiber optic lines for datacommunication and the rate at which data can be read from and stored todata storage devices, (e.g., disk drives, tapes, etc.) increases, thereis an increasing need for efficient use of data storage and transmissioncapacity and also for the ability to encode and decode data at highrates.

BRIEF SUMMARY

The following summarizes some aspects of the present disclosure toprovide a basic understanding of the discussed technology. This summaryis not an extensive overview of all contemplated features of thedisclosure, and is intended neither to identify key or critical elementsof all aspects of the disclosure nor to delineate the scope of any orall aspects of the disclosure. Its sole purpose is to present someconcepts of one or more aspects of the disclosure in summary form as aprelude to the more detailed description that is presented later. Afterconsidering this discussion, and particularly after reading the sectionentitled “Detailed Description” one will understand how the features ofthis disclosure provide advantages that include improved communicationsbetween access points and stations in a wireless network.

While encoding efficiency and high data rates are important, for anencoding and/or decoding system to be practical for use in a wide rangeof devices (e.g., consumer devices), it is also important that theencoders and/or decoders can be implemented at reasonable cost.

Communication systems often need to operate at several different rates.Low-density parity-check (LDPC) codes can be used for simpleimplementation to provide coding and/or decoding at different rates. Forexample, higher-rate LDPC codes can be generated by puncturinglower-rate LDPC codes.

As the demand for mobile broadband access continues to increase, thereexists a need for further improvements in NR technology. Preferably,improvements can or should be applicable to other multi-accesstechnologies and the telecommunication standards that employ thesetechnologies. One area for improvements is the area of encoding/decodingfor data transmissions. These improvements (e.g., improved LDPC codes)can be applicable to NR and other access technologies.

Certain aspects of the present disclosure generally relate to methodsand apparatus for compactly describing multiple lifted low-densityparity-check (LDPC) codes.

Certain aspects of the present disclosure provide a method for wirelesscommunications that may be performed by a transmitting device. Themethod generally includes selecting a first lifting size value Z and afirst set of lifting values for generating a first lifted LDPC code. Atransmitting device can generate a first lifted LDPC code by applyingthe first set of lifting values to interconnect edges in Z copies of abase parity check matrix (PCM) having a first number of base variablenodes and a second number of base check nodes to obtain a first liftedPCM corresponding to the first lifted LDPC code (an edge is a connectionbetween a variable node and a check node). A transmitting device candetermine a second set of lifting values for generating a second liftedPCM corresponding to a second lifted LDPC code for a second lifting sizevalue based on the first lifted PCM and the first set of lifting values.A transmitting device can encode a set of information bits based on thefirst lifted LDPC code and/or the second lifted LDPC code to produce acode word and transmits the code word.

Certain aspects of the present disclosure provide an apparatus forwireless communications that may be performed by a transmitting device.The apparatus generally includes means for selecting a first liftingsize value Z and a first set of lifting values for generating a firstlifted LDPC code and means for generating the first lifted LDPC code byapplying the first set of lifting values to interconnect edges in Zcopies of a base PCM having a first number of base variable nodes and asecond number of base check nodes to obtain a first lifted PCMcorresponding to the first lifted LDPC code. The apparatus also includesmeans for determining a second set of lifting values for generating asecond lifted PCM corresponding to a second lifted LDPC code for asecond lifting size value based on the first lifted PCM and the firstset of lifting values; means for encoding a set of information bitsbased on at least one of: the first lifted LDPC code or the secondlifted LDPC code to produce a code word; and means for transmitting thecode word.

Certain aspects of the present disclosure provide an apparatus forwireless communications that may be performed by a transmitting device.The apparatus generally includes at least one processor coupled with amemory. The at least one processor is configured to select a firstlifting size value Z and a first set of lifting values for generating afirst lifted LDPC code and generate the first lifted LDPC code byapplying the first set of lifting values to interconnect edges in Zcopies of a base PCM having a first number of base variable nodes and asecond number of base check nodes to obtain a first lifted PCMcorresponding to the first lifted LDPC code. The at least one processoris also configured to determine a second set of lifting values forgenerating a second lifted PCM corresponding to a second lifted LDPCcode for a second lifting size value based on the first lifted PCM andthe first set of lifting values and encode a set of information bitsbased on at least one of: the first lifted LDPC code or the secondlifted LDPC code to produce a code word. The apparatus includes atransmitter configured to transmit the code word.

Certain aspects of the present disclosure provide a computer readablemedium having computer executable code stored thereon for wirelesscommunications that may be performed by a transmitting device. The codegenerally includes code for selecting a first lifting size value Z and afirst set of lifting values for generating a first lifted LDPC code andcode for generating the first lifted LDPC code by applying the first setof lifting values to interconnect edges in Z copies of a base PCM havinga first number of base variable nodes and a second number of base checknodes to obtain a first lifted PCM corresponding to the first liftedLDPC code. The code also includes code for determining a second set oflifting values for generating a second lifted PCM corresponding to asecond lifted LDPC code for a second lifting size value based on thefirst lifted PCM and the first set of lifting values; code for encodinga set of information bits based on at least one of: the first liftedLDPC code or the second lifted LDPC code to produce a code word; andcode for transmitting the code word.

Other aspects, features, and embodiments of the present disclosure willbecome apparent to those of ordinary skill in the art, upon reviewingthe following description of specific, exemplary aspects of the presentdisclosure in conjunction with the accompanying figures. While featuresof the present disclosure may be discussed relative to certain aspectsand figures below, all aspects of the present disclosure can include oneor more of the advantageous features discussed herein. In other words,while one or more aspects may be discussed as having certainadvantageous features, one or more of such features may also be used inaccordance with the various aspects of the disclosure discussed herein.In similar fashion, while exemplary aspects may be discussed below asdevice, system, or method embodiments such exemplary embodiments can beimplemented in various devices, systems, and methods.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above-recited features of the presentdisclosure can be understood in detail, a more particular description,briefly summarized above, may be had by reference to aspects, some ofwhich are illustrated in the appended drawings. The appended drawingsillustrate only certain typical aspects of this disclosure, however, andare therefore not to be considered limiting of its scope, for thedescription may admit to other equally effective aspects.

FIG. 1 is a block diagram conceptually illustrating an example wirelesscommunication system, in accordance with certain aspects of the presentdisclosure.

FIG. 2 is a block diagram illustrating an example logical architectureof a distributed RAN, in accordance with certain aspects of the presentdisclosure.

FIG. 3 is a diagram illustrating an example physical architecture of adistributed RAN, in accordance with certain aspects of the presentdisclosure.

FIG. 4 is a block diagram conceptually illustrating a design of anexample base station (BS) and user equipment (UE), in accordance withcertain aspects of the present disclosure.

FIG. 5 is a diagram showing examples for implementing a communicationprotocol stack, in accordance with certain aspects of the presentdisclosure.

FIG. 6 illustrates an example of a downlink (DL)-centric subframe, inaccordance with certain aspects of the present disclosure.

FIG. 7 illustrates an example of an uplink (UL)-centric subframe, inaccordance with certain aspects of the present disclosure.

FIG. 8 is a graphical representation of an example low-densityparity-check (LDPC) code, in accordance with certain aspects of thepresent disclosure.

FIG. 8A is a matrix representation of the example LDPC code of FIG. 8,in accordance with certain aspects of the present disclosure.

FIG. 9 is a graphical representation of liftings of the LDPC code ofFIG. 8, in accordance with certain aspects of the present disclosure.

FIG. 10 is an integer representation of a matrix for a quasi-cyclic802.11 LDPC code according to some aspects.

FIG. 11 is a simplified block diagram illustrating an example encoder,in accordance with certain aspects of the present disclosure.

FIG. 12 is a simplified block diagram illustrating an example decoder,in accordance with certain aspects of the present disclosure.

FIG. 13 is a flow diagram illustrating example operations for generatinglifted LDPC codes from a base parity check matrix (PCM) for wirelesscommunications by a transmitting device, in accordance with certainaspects of the present disclosure.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures. Elements disclosed in one embodiment may be beneficiallyutilized on other embodiments without specific recitation.

DETAILED DESCRIPTION

Aspects of the present disclosure provide apparatus, methods, processingsystems, and computer program products for encoding (and/or decoding)for new radio (NR) access technology (e.g., 5G radio access). NR mayrefer to radios configured to operate according to a new air interfaceor fixed transport layer. NR may include support for enhanced mobilebroadband (eMBB) service targeting wide bandwidth (e.g., 80 MHz andbeyond), millimeter wave (mmW) service targeting high carrier frequency(e.g., 60 GHz), massive machine type communications (mMTC) servicetargeting non-backward compatible MTC techniques, and/or missioncritical (MiCr) service targeting ultra-reliable low-latencycommunications (URLLC) service. These services may include latency andreliability requirements for a variety of uses, timing requirements, andother design considerations. NR may use low-density parity-check (LDPC)coding and/or polar codes.

Aspects of the present disclosure provide techniques and apparatus forcompactly describing LDPC code structure. In aspects, a single basegraph or parity check matrix (PCM) can be stored for a set of liftingsizes (sometimes referred to as a family of liftings or a family oflifted LDPC codes). The PCM may correspond to one of the liftings forthe set of liftings (e.g., the smallest or largest lifting) and theother members of the family can be generated based on a stored PCM usingan operation (e.g., such as a floor operation or a modulo operation). Inaspects, the same PCM can be used for members of the family of codes. Inaspects, PCM for different families of codes can be generated based onthe lifting values associated with one family.

Various aspects of the disclosure are described more fully hereinafterwith reference to the accompanying drawings. This disclosure may,however, be embodied in many different forms and should not be construedas limited to any specific structure or function presented throughoutthis disclosure. Rather, these aspects are provided so that thisdisclosure will be thorough and complete, and will fully convey thescope of the disclosure to those skilled in the art. Based on theteachings herein one skilled in the art should appreciate that the scopeof the disclosure is intended to cover any aspect of the disclosuredisclosed herein, whether implemented independently of or combined withany other aspect of the disclosure. For example, an apparatus may beimplemented or a method may be practiced using any number of the aspectsset forth herein. In addition, the scope of the disclosure is intendedto cover such an apparatus or method which is practiced using otherstructure, functionality, or structure and functionality in addition toor other than the various aspects of the disclosure set forth herein. Itshould be understood that any aspect of the disclosure disclosed hereinmay be embodied by one or more elements of a claim. The word “exemplary”is used herein to mean “serving as an example, instance, orillustration.” Any aspect described herein as “exemplary” is notnecessarily to be construed as preferred or advantageous over otheraspects.

Although particular aspects are described herein, many variations andpermutations of these aspects fall within the scope of the disclosure.Although some benefits and advantages of the preferred aspects arementioned, the scope of the disclosure is not intended to be limited toparticular benefits, uses, or objectives. Rather, aspects of thedisclosure are intended to be broadly applicable to different wirelesstechnologies, system configurations, networks, and transmissionprotocols, some of which are illustrated by way of example in thefigures and in the following description of the preferred aspects. Thedetailed description and drawings are merely illustrative of thedisclosure rather than limiting, the scope of the disclosure beingdefined by the appended claims and equivalents thereof.

The techniques described herein may be used for various wirelesscommunication networks such as Code Division Multiple Access (CDMA)networks, Time Division Multiple Access (TDMA) networks, FrequencyDivision Multiple Access (FDMA) networks, Orthogonal FDMA (OFDMA)networks, Single-Carrier FDMA (SC-FDMA) networks, etc. The terms“networks” and “systems” are often used interchangeably. A CDMA networkmay implement a radio technology such as Universal Terrestrial RadioAccess (UTRA), CDMA2000, etc. UTRA includes Wideband-CDMA (W-CDMA) andLow Chip Rate (LCR). CDMA2000 covers IS-2000, IS-95, and IS-856standards. A TDMA network may implement a radio technology such asGlobal System for Mobile Communications (GSM). An OFDMA network mayimplement a radio technology such as Evolved UTRA (E-UTRA), IEEE 802.11,IEEE 802.16, IEEE 802.20, Flash-OFDM®, etc. UTRA, E-UTRA, and GSM arepart of Universal Mobile Telecommunication System (UMTS). 3GPP LTE andLTE-Advanced (LTE-A) are releases of UMTS that use E-UTRA. UTRA, E-UTRA,UMTS, LTE, LTE-A and GSM are described in documents from an organizationnamed “3rd Generation Partnership Project” (3GPP). CDMA2000 is describedin documents from an organization named “3rd Generation PartnershipProject 2” (3GPP2). NR is an emerging wireless communications technologyunder development in conjunction with the 5G Technology Forum (5GTF).These communications networks are merely listed as examples of networksin which the techniques described in this disclosure may be applied;however, this disclosure is not limited to the above-describedcommunications network.

For clarity, while aspects may be described herein using terminologycommonly associated with 3G and/or 4G or LTE wireless technologies,aspects of the present disclosure can be applied in othergeneration-based communication systems, such as 5G and later, includingNR technologies.

An Example Wireless Communication System

FIG. 1 illustrates an example communications network 100 in whichaspects of the present disclosure may be performed. Wirelesscommunications network 100 may be a new radio (NR) or 5G network.Wireless communications network 100 may include a transmitting devicesuch as a user equipment (UE) 120 or a base station (BS) 110. Thetransmitting device may perform encoding according to aspects describedherein using lifted LDPC codes that may be compactly described (e.g.,determined/generated/stored), and a receiving device (e.g., a UE 120 ora BS 110) can perform corresponding decoding operations. For example,the transmitting device can select at least one lifting size value forgenerating a group of lifted LDPC codes comprising copies of a base LDPCcode defined by a base matrix having a first number of base variablenodes and a second number of base check nodes. The lifting size value isselected from a range of values. The transmitting device can generatethe base matrix based on a lifting value of a set of lifting valuesassociated with the selected lifting size value and generate a matrixfor a different lifting size value in the group based on the basematrix.

As illustrated in FIG. 1, wireless communications network 100 mayinclude a number of BSs 110 and other network entities. ABS may be astation that communicates with UEs. Each BS 110 may providecommunication coverage for a particular geographic area. In 3GPP, theterm “cell” can refer to a coverage area of a Node B and/or a Node Bsubsystem serving this coverage area, depending on the context in whichthe term is used. In NR systems, the term “cell” and gNB, Node B, 5G NB,AP, NR BS, NR BS, TRP, etc., may be interchangeable. In some examples, acell may not necessarily be stationary, and the geographic area of thecell may move according to the location of a mobile BS. In someexamples, the BSs may be interconnected to one another and/or to one ormore other BSs or network nodes (not shown) in wireless communicationsnetwork 100 through various types of backhaul interfaces such as adirect physical connection, a virtual network, or the like using anysuitable transport network.

In general, any number of wireless networks may be deployed in a givengeographic area. Each wireless network may support a particular radioaccess technology (RAT) and may operate on one or more frequencies. ARAT may also be referred to as a radio technology, an air interface,etc. A frequency may also be referred to as a carrier, a frequencychannel, etc. Each frequency may support a single RAT in a givengeographic area in order to avoid interference between wireless networksof different RATs. In some cases, NR or 5G RAT networks may be deployed.

A BS may provide communication coverage for a macro cell, a pico cell, afemto cell, and/or other types of cell. A macro cell may cover arelatively large geographic area (e.g., several kilometers in radius)and may allow unrestricted access by UEs with service subscription. Apico cell may cover a relatively small geographic area and may allowunrestricted access by UEs with service subscription. A femto cell maycover a relatively small geographic area (e.g., a home) and may allowrestricted access by UEs having association with the femto cell (e.g.,UEs in a Closed Subscriber Group (CSG), UEs for users in the home,etc.). ABS for a macro cell may be referred to as a macro BS. ABS for apico cell may be referred to as a pico BS. A BS for a femto cell may bereferred to as a femto BS or a home BS. In the example shown in FIG. 1,BS 110 a, BS 110 b, and BS 110 c may be macro BSs for the macro cell 102a, macro cell 102 b, and macro cell 102 c, respectively. BS 110 x may bea pico BS for pico cell 102 x. BS 110 y and BS 110 z may be femto BS forthe femto cell 102 y and femto cell 102 z, respectively. ABS may supportone or multiple (e.g., three) cells.

Wireless communications network 100 may also include relay stations. Arelay station is a station that receives a transmission of data and/orother information from an upstream station (e.g., a BS 110 or a UE 120)and sends a transmission of the data and/or other information to adownstream station (e.g., a UE 120 or a BS 110). A relay station mayalso be a UE that relays transmissions for other UEs. In the exampleshown in FIG. 1, relay station 110 r may communicate with BS 110 a andUE 120 r in order to facilitate communication between BS 110 a and UE120 r. A relay station may also be referred to as a relay, a relay eNB,etc.

Wireless communications network 100 may be a heterogeneous network thatincludes BSs of different types, for example, macro BS, pico BS, femtoBS, relays, etc. These different types of BSs may have differenttransmit power levels, different coverage areas, and different impact oninterference in the wireless communications network 100. For example, amacro BS may have a high transmit power level (e.g., 20 Watts) whereaspico BS, femto BS, and relays may have a lower transmit power level(e.g., 1 Watt).

Wireless communications network 100 may support synchronous orasynchronous operation. For synchronous operation, the BSs may havesimilar frame timing, and transmissions from different BSs may beapproximately aligned in time. For asynchronous operation, the BSs mayhave different frame timing, and transmissions from different BSs maynot be aligned in time. The techniques described herein may be used forboth synchronous and asynchronous operation.

Network controller 130 may couple to a set of BSs and providecoordination and control for these BSs. Network controller 130 maycommunicate with BSs 110 via a backhaul. BSs 110 may also communicatewith one another, e.g., directly or indirectly via wireless or wirelinebackhaul.

UEs 120 (e.g., UE 120 x, UE 120 y, etc.) may be dispersed throughoutwireless communications network 100, and each UE may be stationary ormobile. A UE may also be referred to as a mobile station, a terminal, anaccess terminal, a subscriber unit, a station, a Customer PremisesEquipment (CPE), a cellular phone, a smart phone, a personal digitalassistant (PDA), a wireless modem, a wireless communication device, ahandheld device, a laptop computer, a cordless phone, a wireless localloop (WLL) station, a tablet, a camera, a gaming device, a netbook, asmartbook, an ultrabook, a medical device or medical equipment, abiometric sensor/device, a wearable device such as a smart watch, smartclothing, smart glasses, a smart wrist band, smart jewelry (e.g., asmart ring, a smart bracelet, etc.), an entertainment device (e.g., amusic device, a video device, a satellite radio, etc.), a vehicularcomponent or sensor, a smart meter/sensor, industrial manufacturingequipment, a global positioning system device, or any other suitabledevice that is configured to communicate via a wireless or wired medium.Some UEs may be considered evolved or machine-type communication (MTC)devices or evolved MTC (eMTC) devices. MTC and eMTC UEs include, forexample, robots, drones, remote devices, sensors, meters, monitors,location tags, etc., that may communicate with a BS, another device(e.g., remote device), or some other entity. A wireless node mayprovide, for example, connectivity for or to a network (e.g., a widearea network such as Internet or a cellular network) via a wired orwireless communication link. Some UEs may be consideredInternet-of-Things (IoT) devices.

In FIG. 1, a solid line with double arrows indicates desiredtransmissions between a UE and a serving BS, which is a BS designated toserve the UE on the downlink and/or uplink. A finely dashed line withdouble arrows indicates interfering transmissions between a UE and a BS.

Certain wireless networks (e.g., LTE) utilize orthogonal frequencydivision multiplexing (OFDM) on the downlink and single-carrierfrequency division multiplexing (SC-FDM) on the uplink. OFDM and SC-FDMpartition the system bandwidth into multiple (K) orthogonal subcarriers,which are also commonly referred to as tones, bins, etc. Each subcarriermay be modulated with data. In general, modulation symbols are sent inthe frequency domain with OFDM and in the time domain with SC-FDM. Thespacing between adjacent subcarriers may be fixed, and the total numberof subcarriers (K) may be dependent on the system bandwidth. Forexample, the spacing of the subcarriers may be 15 kHz and the minimumresource allocation (called a “resource block” (RB)) may be 12subcarriers (i.e., 180 kHz). Consequently, the nominal Fast FourierTransform (FFT) size may be equal to 128, 256, 512, 1024 or 2048 forsystem bandwidth of 1.25 MHz, 2.5 MHz, 5 MHz, 10 MHz, or 20 MHz,respectively. The system bandwidth may also be partitioned intosubbands. For example, a subband may cover 1.08 MHz (i.e., 6 RBs), andthere may be 1, 2, 4, 8 or 16 subbands for system bandwidth of 1.25 MHz,2.5 MHz, 5 MHz, 10 MHz, or 20 MHz, respectively.

NR may utilize OFDM with a CP on uplink and downlink and include supportfor half-duplex operation using TDD. A single component carrierbandwidth of 100 MHz may be supported. NR RBs may span 12 subcarrierswith a subcarrier bandwidth of 75 kHz over a 0.1 ms duration. Each radioframe may consist of 50 subframes with a length of 10 ms. Consequently,each subframe may have a length of 0.2 ms. Each subframe may indicate alink direction (i.e., downlink or uplink) for data transmission and thelink direction for each subframe may be dynamically switched. Eachsubframe may include DL/UL data as well as DL/UL control data. UL and DLsubframes for NR may be as described in more detail below with respectto FIGS. 6 and 7. Beamforming may be supported and beam direction may bedynamically configured. MIMO transmissions with precoding may also besupported. MIMO configurations in the DL may support up to 8 transmitantennas with multi-layer DL transmissions up to 8 streams and up to 2streams per UE. Multi-layer transmissions with up to 2 streams per UEmay be supported. Aggregation of multiple cells may be supported with upto 8 serving cells. Alternatively, NR may support a different airinterface, other than an OFDM-based.

In some examples, access to the air interface may be scheduled. Forexample, a scheduling entity (e.g., a BS 110 or UE 120) allocatesresources for communication among some or all devices and equipmentwithin its service area or cell. Within the present disclosure, asdiscussed further below, the scheduling entity may be responsible forscheduling, assigning, reconfiguring, and releasing resources for one ormore subordinate entities. That is, for scheduled communication,subordinate entities utilize resources allocated by the schedulingentity. BSs are not the only entities that may function as a schedulingentity. That is, in some examples, a UE may function as a schedulingentity, scheduling resources for one or more subordinate entities (e.g.,one or more other UEs). In this example, the UE is functioning as ascheduling entity, and other UEs utilize resources scheduled by the UEfor wireless communication. A UE may function as a scheduling entity ina peer-to-peer (P2P) network, and/or in a mesh network. In a meshnetwork example, UEs may optionally communicate directly with oneanother in addition to communicating with the scheduling entity.

Thus, in a wireless communication network with a scheduled access totime-frequency resources and having a cellular configuration, a P2Pconfiguration, and a mesh configuration, a scheduling entity and one ormore subordinate entities may communicate utilizing the scheduledresources.

The NR radio access network (RAN) may include one or more central units(CU) and distributed units (DUs). A NR BS (e.g., a gNB, a 5G NB, a NB, a5G NB, a TRP, an AP) may correspond to one or multiple BSs. NR cells canbe configured as access cells (ACells) or data only cells (DCells).DCells may be cells used for carrier aggregation or dual connectivity,but not used for initial access, cell selection/reselection, orhandover.

FIG. 2 illustrates an example logical architecture of a distributed RAN200, which may be implemented in wireless communications system 100illustrated in FIG. 1. 5G access node (AN) 206 may include access nodecontroller (ANC) 202. ANC 202 may be a CU of distributed RAN 200. Abackhaul interface to next generation core network (NG-CN) 204 mayterminate at ANC 202. A backhaul interface to neighboring nextgeneration access nodes (NG-ANs) may terminate at ANC 202. ANC 202 mayinclude one or more TRPs 208.

TRPs 208 comprise DUs. TRPs 208 may be connected to one ANC (ANC 202) ormore than one ANC (not illustrated). For example, for RAN sharing, radioas a service (RaaS), and service specific AND deployments, the TRP maybe connected to more than one ANC 202. A TRP 208 may include one or moreantenna ports. TRPs 208 may be configured to individually (e.g., dynamicselection) or jointly (e.g., joint transmission) serve traffic to a UE(e.g., a UE 120).

Example logical architecture of the distributed RAN 200 may be used toillustrate fronthaul definition. The logical architecture may supportfronthauling solutions across different deployment types. For example,the logical architecture may be based on transmit network capabilities(e.g., bandwidth, latency, and/or jitter). The logical architecture mayshare features and/or components with LTE. NG-AN 210 may support dualconnectivity with NR. NG-AN 210 may share a common fronthaul for LTE andNR. The logical architecture may enable cooperation between and amongTRPs 208. For example, cooperation may be pre-configured within a TRP208 and/or across TRPs 208 via ANC 202. There may be no inter-TRPinterface.

The logical architecture for distributed RAN 200 may include a dynamicconfiguration of split logical functions. As will be described in moredetail with reference to FIG. 5, the Radio Resource Control (RRC) layer,Packet Data Convergence Protocol (PDCP) layer, Radio Link Control (RLC)layer, Medium Access Control (MAC) layer, and a Physical (PHY) layersmay be placed at the DU (e.g., a TRP 208) or the CU (e.g., ANC 202).

FIG. 3 illustrates an example physical architecture of a distributed RAN300, according to aspects of the present disclosure. As shown in FIG. 3,distributed RAN 300 includes centralized core network unit (C-CU) 302,centralized RAN unit (C-RU) 304, and DU 306.

C-CU 302 may host core network functions. C-CU 302 may be centrallydeployed. C-CU 302 functionality may be offloaded (e.g., to advancedwireless services (AWS)), in an effort to handle peak capacity. C-RU 304may host one or more ANC functions. Optionally, C-RU 304 may host corenetwork functions locally. C-RU 304 may have a distributed deployment.C-RU 304 may be located near an edge the network. DU 306 may host one ormore TRPs (edge node (EN), an edge unit (EU), a radio head (RH), a smartradio head (SRH), or the like). DU 306 may be located at edges of thenetwork with radio frequency (RF) functionality.

FIG. 4 illustrates example components of the BS 110 and the UE 120illustrated in FIG. 1, which may be used to implement aspects of thepresent disclosure for high performance, flexible, and compact LDPCcoding. One or more of the components of BS 110 and UE 120 illustratedin FIG. 4 may be used to practice aspects of the present disclosure. Forexample, antenna(s) 452 a-454 r, Demodulator(s)/Modulator(s) 454 a-454r, TX MIMO processor 466, Receive Processor 458, Transmit Processor 464,and/or Controller/Processor 480 of UE 120 and/or antenna(s) 434 a 434 t,Demodulator(s)/Modulator(s) 432 a-434 t, TX MIMO Processors 430,Transmit Processor 420, Receive Processor 438, and/orController/Processor 440 of BS 110 may be used to perform the operations1300-1600 described herein and illustrated with reference to FIGS.13-16, respectively.

For a restricted association scenario, BS 110 may be macro BS 110 c inFIG. 1, and UE 120 may be UE 120 y. BS 110 may also be a BS of someother type. BS 110 may be equipped with antennas 434 a through 434 t andUE 120 may be equipped with antennas 452 a through 452 r.

At BS 110, transmit processor 420 may receive data from data source 412and control information from controller/processor 440. The controlinformation may be for the Physical Broadcast Channel (PBCH), PhysicalControl Format Indicator Channel (PCFICH), Physical Hybrid ARQ IndicatorChannel (PHICH), Physical Downlink Control Channel (PDCCH), or othercontrol channel or signal. The data may be for the Physical DownlinkShared Channel (PDSCH), or other data channel or signal. Transmitprocessor 420 may process (e.g., encode and symbol map) the data andcontrol information to obtain data symbols and control symbols,respectively. For example, transmit processor 420 may encode theinformation bits using LPDC code designs discussed in greater detailbelow. Transmit processor 420 may also generate reference symbols, forexample, for the primary synchronization signal (PSS), secondarysynchronization signal (SSS), and cell-specific reference signal (CRS).Transmit (TX) multiple-input multiple-output (MIMO) processor 430 mayperform spatial processing (e.g., precoding) on the data symbols, thecontrol symbols, and/or the reference symbols, if applicable, and mayprovide output symbol streams to the modulators (MODs) 432 a through 432t. Each modulator 432 may process a respective output symbol stream(e.g., for OFDM, etc.) to obtain an output sample stream. Each modulator432 may further process (e.g., convert to analog, amplify, filter, andupconvert) the output sample stream to obtain a downlink signal.Downlink signals from modulators 432 a through 432 t may be transmittedvia antennas 434 a through 434 t, respectively.

At UE 120, antennas 452 a through 452 r may receive the downlink signalsfrom BS 110 and may provide received signals to the demodulators(DEMODs) 454 a through 454 r, respectively. Each demodulator 454 maycondition (e.g., filter, amplify, downconvert, and digitize) arespective received signal to obtain input samples. Each demodulator 454may further process the input samples (e.g., for OFDM, etc.) to obtainreceived symbols. MIMO detector 456 may obtain received symbols from allthe demodulators 454 a through 454 r, perform MIMO detection on thereceived symbols if applicable, and provide detected symbols. Receiveprocessor 458 may process (e.g., demodulate, deinterleave, and decode)the detected symbols, provide decoded data for UE 120 to a data sink460, and provide decoded control information to controller/processor480.

On the uplink, at UE 120, transmit processor 464 may receive and processdata (e.g., for the Physical Uplink Shared Channel (PUSCH) or other datachannel or signal) from data source 462 and control information (e.g.,for the Physical Uplink Control Channel (PUCCH) or other control channelor signal) from controller/processor 480. Transmit processor 464 mayalso generate reference symbols for a reference signal. The symbols fromtransmit processor 464 may be precoded by TX MIMO processor 466 ifapplicable, further processed by demodulators 454 a through 454 r (e.g.,for SC-FDM, etc.), and transmitted to BS 110. At BS 110, the uplinksignals from the UE 120 may be received by antennas 434, processed bymodulators 432, detected by MIMO detector 436 if applicable, and furtherprocessed by receive processor 438 to obtain decoded data and controlinformation sent by UE 120. Receive processor 438 may provide thedecoded data to data sink 439 and the decoded control information tocontroller/processor 440.

Memory 442 may store data and program codes for BS 110 and memory 482may store data and program codes for UE 120. Scheduler 444 may scheduleUEs for data transmission on the downlink and/or uplink.

FIG. 5 illustrates a diagram 500 showing examples for implementing acommunications protocol stack per aspects of the present disclosure. Theillustrated communications protocol stacks may be implemented by devicesoperating in a in a 5G system (e.g., a system that supports uplink-basedmobility). Diagram 500 illustrates a communications protocol stackincluding RRC layer 510, PDCP layer 515, RLC layer 520, MAC layer 525,and PHY layer 530. In an example, the layers of a protocol stack may beimplemented as separate modules of software, portions of a processor orASIC, portions of non-collocated devices connected by a communicationslink, or various combinations thereof. Collocated and non-collocatedimplementations may be used, for example, in a protocol stack for anetwork access device (e.g., ANs, CUs, and/or DUs) or a UE.

A first option 505-a shows a split implementation of a protocol stack,in which implementation of the protocol stack is split between acentralized network access device (e.g., ANC 202) and distributednetwork access device (e.g., DU 208). In the first option 505-a, RRClayer 510 and PDCP layer 515 may be implemented by the CU, and RLC layer520, MAC layer 525, and PHY layer 530 may be implemented by the DU. Invarious examples, the CU and the DU may be collocated or non-collocated.The first option 505-a may be useful in a macro cell, micro cell, orpico cell deployment.

A second option 505-b shows a unified implementation of a protocolstack, in which the protocol stack is implemented in a single networkaccess device (e.g., access node (AN), NR BS, a NR NBa network node(NN), TRP, gNB, etc.). In the second option, RRC layer 510, PDCP layer515, RLC layer 520, MAC layer 525, and PHY layer 530 may each beimplemented by the AN. The second option 505-b may be useful in a femtocell deployment.

Regardless of whether a network access device implements part or all ofa protocol stack, a UE may implement the entire protocol stack (e.g.,RRC layer 510, PDCP layer 515, RLC layer 520, MAC layer 525, and PHYlayer 530).

FIG. 6 is a diagram showing an example of a DL-centric subframe 600. TheDL-centric subframe 600 may include control portion 602. Control portion602 may exist in the initial or beginning portion of DL-centric subframe600. Control portion 602 may include various scheduling informationand/or control information corresponding to various portions ofDL-centric subframe 600. In some configurations, control portion 602 maybe a physical DL control channel (PDCCH), as shown in FIG. 6. DL-centricsubframe 600 may also include DL data portion 604. DL data portion 604may be referred to as the payload of DL-centric subframe 600. DL dataportion 604 may include the communication resources utilized tocommunicate DL data from the scheduling entity (e.g., UE or BS) to thesubordinate entity (e.g., UE). In some configurations, DL data portion604 may be a physical DL shared channel (PDSCH).

DL-centric subframe 600 may also include common UL portion 606. CommonUL portion 606 may be referred to as an UL burst, a common UL burst,and/or various other suitable terms. Common UL portion 606 may includefeedback information corresponding to various other portions ofDL-centric subframe 600. For example, common UL portion 606 may includefeedback information corresponding to control portion 602. Non-limitingexamples of feedback information may include an acknowledgment (ACK)signal, a negative acknowledgment (NACK) signal, a HARQ indicator,and/or various other suitable types of information. Common UL portion606 may additionally or alternatively include information, such asinformation pertaining to random access channel (RACH) procedures,scheduling requests (SRs), and various other suitable types ofinformation. As illustrated in FIG. 6, the end of DL data portion 604may be separated in time from the beginning of common UL portion 606.This time separation may be referred to as a gap, a guard period, aguard interval, and/or various other suitable terms. This separationprovides time for the switchover from DL communication (e.g., receptionoperation by the subordinate entity (e.g., UE)) to UL communication(e.g., transmission by the subordinate entity (e.g., UE)). The foregoingis merely one example of a DL-centric subframe and alternativestructures having similar features may exist without necessarilydeviating from the aspects described herein.

FIG. 7 is a diagram showing an example of an UL-centric subframe 700.UL-centric subframe 700 may include control portion 702. Control portion702 may exist in the initial or beginning portion of UL-centric subframe700. Control portion 702 in FIG. 7 may be similar to control portion 602described above with reference to FIG. 6. UL-centric subframe 700 mayalso include UL data portion 704. UL data portion 704 may be referred toas the payload of UL-centric subframe 700. UL data portion 704 may referto the communication resources utilized to communicate UL data from thesubordinate entity (e.g., UE) to the scheduling entity (e.g., UE or BS).In some configurations, control portion 702 may be a PDCCH.

As illustrated in FIG. 7, the end of control portion 702 may beseparated in time from the beginning of UL data portion 704. This timeseparation may be referred to as a gap, guard period, guard interval,and/or various other suitable terms. This separation provides time forthe switchover from DL communication (e.g., reception operation by thescheduling entity) to UL communication (e.g., transmission by thescheduling entity). UL-centric subframe 700 may also include common ULportion 706. Common UL portion 706 in FIG. 7 may be similar to thecommon UL portion 606 described above with reference to FIG. 6. CommonUL portion 706 may additionally or alternatively include informationpertaining to channel quality indicator (CQI), sounding referencesignals (SRSs), and various other suitable types of information. Theforegoing is merely one example of an UL-centric subframe andalternative structures having similar features may exist withoutnecessarily deviating from the aspects described herein.

In some circumstances, two or more subordinate entities (e.g., UEs) maycommunicate with each other using sidelink signals. Real-worldapplications of such sidelink communications may include public safety,proximity services, UE-to-network relaying, vehicle-to-vehicle (V2V)communications, Internet-of-Everything (IoE) communications, IoTcommunications, mission-critical mesh, and/or various other suitableapplications. Generally, a sidelink signal may refer to a signalcommunicated from one subordinate entity (e.g., UE1) to anothersubordinate entity (e.g., UE2) without relaying that communicationthrough the scheduling entity (e.g., UE or BS), even though thescheduling entity may be utilized for scheduling and/or controlpurposes. In some examples, the sidelink signals may be communicatedusing a licensed spectrum (unlike wireless local area networks (WLAN),which typically use an unlicensed spectrum).

A UE may operate in various radio resource configurations, including aconfiguration associated with transmitting pilots using a dedicated setof resources (e.g., a radio resource control (RRC) dedicated state,etc.) or a configuration associated with transmitting pilots using acommon set of resources (e.g., an RRC common state, etc.). Whenoperating in the RRC dedicated state, the UE may select a dedicated setof resources for transmitting a pilot signal to a network. Whenoperating in the RRC common state, the UE may select a common set ofresources for transmitting a pilot signal to the network. In eithercase, a pilot signal transmitted by the UE may be received by one ormore network access devices, such as an AN, or a DU, or portionsthereof. Each receiving network access device may be configured toreceive and measure pilot signals transmitted on the common set ofresources, and also receive and measure pilot signals transmitted ondedicated sets of resources allocated to the UEs for which the networkaccess device is a member of a monitoring set of network access devicesfor the UE. One or more of the receiving network access devices, or a CUto which receiving network access device(s) transmit the measurements ofthe pilot signals, may use the measurements to identify serving cellsfor the UEs, or to initiate a change of serving cell for one or more ofthe UEs.

Example Error Correction Coding

Many communications systems use error-correcting codes. Error correctingcodes generally compensate for the intrinsic unreliability ofinformation transfer (e.g., over the air medium) in these systems byintroducing redundancy into the data stream. Low-density parity-check(LDPC) codes are one type of error correcting codes which use aniterative coding system. Gallager codes are an example of “regular” LDPCcodes. Regular LDPC codes are linear block codes in which most of theelements of its parity check matrix H are ‘0’.

LDPC codes can be represented by bipartite graphs (often referred to as“Tanner graphs”). In a bipartite graph, a set of variable nodescorresponds to bits of a code word (e.g., information bits or systematicbits), and a set of check nodes correspond to a set of parity-checkconstraints that define the code. Edges in the graph connect variablenodes to check nodes. Thus, the nodes of the graph are separated intotwo distinctive sets and with edges connecting nodes of two differenttypes, variable and check.

Graphs as used in LDPC coding may be characterized in a variety ofmanners. A lifted code is created by copying a bipartite base graph (G)(or a protograph), a number of times, Z. The number of times is referredto herein as the lifting, lifting size, or lifting size value. Avariable node and a check node are considered “neighbors” if they areconnected by an “edge” (i.e., the line connecting the variable node andthe check node) in the graph. In addition, for each edge (e) of thebipartite base graph (G), a permutation (generally an integer valueassociated with the edge permutation that is represented by k andreferred to as the lifting value) is applied to the Z copies of edge (e)to interconnect the Z copies of G. A bit sequence having a one-to-oneassociation with the variable node sequence is a valid code word if andonly if, for each check node, the bits associated with all neighboringvariable nodes sum to 0 modulo 2 (i.e., they include an even number ofl's). The resulting LDPC code may be quasi-cyclic (QC) if thepermutations (liftings values) used are cyclic.

FIGS. 8-8A show graphical and matrix representations, respectively, ofan example LDPC code, in accordance with certain aspects of the presentdisclosure. For example, FIG. 8 shows a bipartite graph 800 representingan example LDPC code. Bipartite graph 800 includes a set of fivevariable nodes 810 (represented by circles) connected to four checknodes 820 (represented by squares). Edges in bipartite graph 800 connectvariable nodes 810 to check nodes 820 (the edges are represented by thelines connecting variable nodes 810 to check nodes 820). Bipartite graph800 consists of |V|=5 variable nodes and |C|=4 check nodes, connected by|E|=12 edges.

Bipartite graph 800 may be represented by a simplified adjacency matrix,which may also be known as a parity check matrix (PCM). FIG. 8A shows amatrix representation 800A of bipartite graph 800. Matrix representation800A includes a PCM H and a code word vector x, where x₁-x₅ representbits of the code word x. H is used for determining whether a receivedsignal was normally decoded. H has C rows corresponding to j check nodesand V columns corresponding to i variable nodes (i.e., a demodulatedsymbol), where the rows represent the equations and the columnsrepresents the bits of the code word. In FIG. 8A, matrix H has four rowsand five columns corresponding to four check nodes and five variablenodes, respectively. If a j-th check node is connected to an i-thvariable node by an edge (i.e., the two nodes are neighbors), then thereis a 1 in the i-th column and in the j-th row of the parity check matrixH. That is, the intersection of an i-th row and a j-th column contains a“1” where an edge joins the corresponding vertices and a “0” where thereis no edge. The code word vector x represents a valid code word if andonly if H_(x)=0, for example, if for each constraint node, the bitsneighboring the constraint, via their association with variable nodes,sum to 0 modulo 2 (i.e., they comprise an even number of 1′a). Thus, ifthe code word is received correctly, then H_(x)=0 (mod 2). When theproduct of a coded received signal and the PCM H becomes ‘0’, thissignifies that no error has occurred.

The number of demodulated symbols or variable nodes is the LDPC codelength. The number of non-zero elements in a row (column) is defined asthe row (column) weight d(c)d(v). The degree of a node refers to thenumber of edges connected to that node. For example, as shown in FIG. 8,the variable node 801 has three degrees of connectivity, with edgesconnected to check nodes 811, 812, and 813. Variable node 802 has threedegrees of connectivity, with edges connected to check nodes 811, 813,and 814. Variable node 803 has two degrees of connectivity, with edgesconnected to check nodes 811 and 814. Variable node 804 has two degreesof connectivity, with edges connected to check nodes 812 and 814. Andvariable node 805 has two degrees of connectivity, with edges connectedto check nodes 812 and 813. This feature is illustrated in the matrix Hshown in FIG. 8A where the number of edges incident to a variable node810 is equal to the number of l's in the corresponding column and iscalled the variable node degree d(v). Similarly, the number of edgesconnected with a check node 820 is equal to the number of ones in acorresponding row and is called the check node degree d(c). For example,as shown in FIG. 8A, the first column in the matrix H corresponds to thevariable node 801 and the corresponding entries in the column (1, 1, 1,0) indicates the edge connections to the check nodes 811, 812, and 813,while the 0 indicates that there is not an edge to check node 814. Theentries in the second, third, fourth, and fourth columns of H representthe edge connections of the variable nodes 802, 803, 804, and 805,respectively, to the check nodes.

A regular graph or a regular code is one for which all variable nodeshave the same degree and all constraint nodes have the same degree. Onthe other hand, an irregular code has constraint nodes and/or variablenodes of differing degrees. For example, some variable nodes may be ofdegree 4, others of degree 3, and still others of degree 2.

“Lifting” enables LDPC codes to be implemented using parallel encodingand/or decoding implementations while also reducing the complexitytypically associated with large LDPC codes. Lifting helps enableefficient parallelization of LDPC decoders while still having arelatively compact description. More specifically, lifting is atechnique for generating a relatively large LDPC code from multiplecopies of a smaller base code. For example, a lifted LDPC code may begenerated by producing Z of parallel copies of the base graph (e.g.,protograph) and then interconnecting the parallel copies throughpermutations of edge bundles of each copy of the base graph. The basegraph defines the (macro) structure of the code and consists of a number(K) of information bit columns and a number (N) of code bit columns.Lifting the base graph a number of liftings Z results in a final blocklength of KZ. Thus, a larger graph can be obtained by a “copy andpermute” operation where multiple copies of the base graph are made andconnected to form a single lifted graph. For the multiple copies, likeedges are a set of copies of single base edge, are permutated andconnected to form a connected graph Z times larger than the base graph.

FIG. 9 is a bipartite graph illustrating liftings of three copies of thebipartite graph 800 of FIG. 8. Three copies may be interconnected bypermuting like edges among the copies. If the permutations arerestricted to cyclic permutations, then the resulting bipartite graph900 corresponds to a quasi-cyclic LDPC with lifting Z=3. The originalgraph 800 from which three copies were made is referred to herein as thebase graph. To obtain graphs of different sizes, “copy and permute”operation can be applied to the base graph.

A corresponding PCM of the lifted graph can be constructed from theparity check matrix of the base graph by replacing each entry in thebase parity check matrix with a Z×Z matrix. The “0” entries (thosehaving no base edges) are replaced with the 0 matrix and the 1 entries(indicating a base edge) are replaced with a Z×Z permutation matrix. Inthe case of cyclic liftings, the permutations are cyclic permutations.

A cyclically lifted LDPC code can also be interpreted as a code over thering of binary polynomials modulo x^(z)+1. In this interpretation, abinary polynomial, (x)=b₀+b₁x+b₂x²+ . . . +b_(z−1)x^(x−1) may beassociated to each variable node in the base graph. The binary vector(b₀, b₁, b₂, . . . , b_(z−1)) corresponds to the bits associated to Zcorresponding variable nodes in the lifted graph, that is, Z copies of asingle base variable node. A cyclic permutation by k (referred to as alifting value associated to the edges in the graph) of the binary vectoris achieved by multiplying the corresponding binary polynomial by x^(k)where multiplication is taken modulo x^(z)+1. A degree d parity check inthe base graph can be interpreted as a linear constraint on theneighboring binary polynomials B₁(x), . . . , B_(d)(x), written as x^(k)¹ B₁(x)+x^(k) ² B₂(x)+ . . . +x^(k) ^(d) B_(d)(x)=0x^(k) ¹ B₁(x)+x^(k) ²B₂(x)+ . . . +x^(k) ^(d) B_(d)(x)=0, the values, k₁, . . . , k_(d) arethe cyclic lifting values associated to the corresponding edges.

This resulting equation is equivalent to the Z parity checks in thecyclically lifted Tanner graph corresponding to the single associatedparity check in the base graph. Thus, the parity check matrix for thelifted graph can be expressed using the matrix for the base graph inwhich 1 entries are replaced with monomials of the form x^(k) and 0entries are lifted as 0, but now the 0 is interpreted as the 0 binarypolynomial modulo x^(z)+1. Such a matrix may be written by giving thevalue k in place of x^(k). In this case the 0 polynomial is sometimesrepresented as “−1” and sometimes as another character in order todistinguish it from Typically, a square submatrix of the parity checkmatrix represents the parity bits of the code. The complementary columnscorrespond to information bits that, at the time of encoding, are setequal to the information bits to be encoded. The encoding may beachieved by solving for the variables in the aforementioned squaresubmatrix in order to satisfy the parity check equations. The paritycheck matrix H may be partitioned into two parts M and N where M is thesquare portion. Thus, encoding reduces to solving M_(c)=s=Nd where c andd comprise x. In the case of quasi-cyclic codes, or cyclically liftedcodes, the above algebra can be interpreted as being over the ring ofbinary polynomials modulo x^(z)+1. In the case of the 802.11 LDPC codes,which are quasi-cyclic, the encoding submatrix M has an integerrepresentation as shown in FIG. 10.

A received LDPC code word can be decoded to produce a reconstructedversion of the original code word. In the absence of errors, or in thecase of correctable errors, decoding can be used to recover the originaldata unit that was encoded. Redundant bits may be used by decoders todetect and correct bit errors. LDPC decoder(s) generally operate byiteratively performing local calculations and passing those results byexchanging messages within the bipartite graph along the edges, andupdating these messages by performing computations at the nodes based onthe incoming messages. These steps may be repeated several times. Forexample, each variable node 810 in the graph 800 may initially beprovided with a “soft bit” (e.g., representing the received bit of thecode word) that indicates an estimate of the associated bit's value asdetermined by observations from the communications channel. Using thesesoft bits the LDPC decoders may update messages by iteratively readingthem, or some portion thereof, from memory and writing an updatedmessage, or some portion thereof, back to, memory. The update operationsare typically based on the parity check constraints of the correspondingLDPC code. In implementations for lifted LDPC codes, messages on likeedges are often processed in parallel.

LDPC codes designed for high speed applications often use quasi-cyclicconstructions with large lifting factors and relatively small basegraphs to support high parallelism in encoding and decoding operations.LDPC codes with higher code rates (e.g., the ratio of the message lengthto the codeword length) tend to have relatively fewer parity checks. Ifthe number of base parity checks is smaller than the degree of avariable node (e.g., the number of edges connected to a variable node),then, in the base graph, that variable node is connected to at least oneof the base parity checks by two or more edges (e.g., the variable nodemay have a “double edge”). If the number of base parity checks issmaller than the degree of a variable node (e.g., the number of edgesconnected to a variable node), then, in the base graph, that variablenode is connected to at least one of the base parity checks by two ormore edges. Having a base variable node and a base check node connectedby two or more edges is generally undesirable for parallel hardwareimplementation purposes. For example, such double edges may result inmultiple concurrent read and write operations to the same memorylocations, which in turn may create data coherency problems. A doubleedge in a base LDPC code may trigger parallel reading of the same softbit value memory location twice during a single parallel parity checkupdate. Thus, additional circuitry is typically needed to combine thesoft bit values that are written back to memory, so as to properlyincorporate both updates. Eliminating double edges in the LDPC codehelps to avoid this extra complexity.

LDPC code designs based on cyclic lifting can be interpreted, as codesover the ring of polynomials modulo may be binary polynomials modulox^(z)−1, where Z is the lifting size (e.g., the size of the cycle in thequasi-cyclic code). Thus encoding such codes can often be interpreted asan algebraic operation in this ring.

In the definition of standard irregular LDPC code ensembles (degreedistributions) all edges in the Tanner graph representation may bestatistically interchangeable. In other words, there exists a singlestatistical equivalence class of edges. A more detailed discussion oflifted LDPC codes may be found, for example, in the book titled, “ModernCoding Theory,” published Mar. 17, 2008, by Tom Richardson and RuedigerUrbanke. For multi-edge LDPC codes, multiple equivalence classes ofedges may be possible. While in the standard irregular LDPC ensembledefinition, nodes in the graph (both variable and constraint) arespecified by their degree, i.e., the number of edges they are connectedto, in the multi-edge type setting an edge degree is a vector; itspecifies the number of edges connected to the node from each edgeequivalence class (type) independently. A multi-edge type ensemble iscomprised of a finite number of edge types. The degree type of aconstraint node is a vector of (non-negative) integers; the i-th entryof this vector records the number of sockets of the i-th type connectedto such a node. This vector may be referred to as an edge degree. Thedegree type of a variable node has two parts although it can be viewedas a vector of (non-negative) integers. The first part relates to thereceived distribution and will be termed the received degree and thesecond part specifies the edge degree. The edge degree plays the samerole as for constraint nodes. Edges are typed as they pair sockets ofthe same type. The constraint that sockets must pair with sockets oflike type characterizes the multi-edge type concept. In a multi-edgetype description, different node types can have different receiveddistributions (e.g., the associated bits may go through differentchannels).

Puncturing is the act of removing bits from a codeword to yield ashorter codeword. Thus, punctured variable nodes correspond to codewordbits that are not actually transmitted. Puncturing a variable node in anLDPC code creates a shortened code (e.g. due to the removal of a bit),while also effectively removing a check node. Specifically, for a matrixrepresentation of an LDPC, code, including bits to be punctured, wherethe variable node to be punctured has a degree of one (such arepresentation may be possible through row combining provided the codeis proper), puncturing the variable node removes the associated bit fromthe code and effectively removes its single neighboring check node fromthe graph. As a result, the number of check nodes in the graph isreduced by one.

FIG. 11 is a simplified block diagram illustrating an encoder, inaccordance with certain aspects of the present disclosure. FIG. 11 is asimplified block diagram 1100 illustrating a portion of radio frequency(RF) modem 1150 that may be configured to provide a signal including anencoded message for wireless transmission. In one example, convolutionalencoder 1102 in a BS 110 (or a LTE 120 on the reverse path) receivesmessage 1120 for transmission. Message 1120 may contain data and/orencoded voice or other content directed to the receiving device. Encoder1102 encodes the message using a suitable modulation and coding scheme(MCS), typically selected based on a configuration defined by BS 110 oranother network entity. Encoded bitstream 1122 produced by encoder 1102may then be selectively punctured by puncturing module 1104, which maybe a separate device or component, or which may be integrated withencoder 1102. Puncturing module 1104 may determine that bitstream 1122should be punctured prior to transmission, or transmitted withoutpuncturing. The decision to puncture bitstream 1122 is typically madebased on network conditions, network configuration, RAN definedpreferences and/or for other reasons. Bitstream 1122 may be puncturedaccording to puncture pattern 1112 and used to encode message 1120.Puncturing module 1104 provides output 1124 to mapper 1106 thatgenerates a sequence of Tx symbols 1126 that are modulated, amplifiedand otherwise processed by Tx chain 1108 to produce an RF signal 1128for transmission through antenna 1110.

Output 1124 of puncturing module 1104 may be the unpunctured bitstream1122 or a punctured version of the bitstream 1122, according to whethermodem portion 1150 is configured to puncture the bitstream 1122. In oneexample, parity and/or other error correction bits may be punctured inoutput 1124 of encoder 1102 in order to transmit message 1120 within alimited bandwidth of the RF channel. In another example, the bitstreammay be punctured to reduce the power needed to transmit message 1120, toavoid interference, or for other network-related reasons. Thesepunctured code word bits are not transmitted.

The decoders and decoding algorithms used to decode LDPC codewordsoperate by exchanging messages within the graph along the edges andupdating these messages by performing computations at the nodes based onthe incoming messages. Each variable node in the graph is initiallyprovided with a soft bit, termed a received value, that indicates anestimate of the associated bit's value as determined by observationsfrom, for example, the communications channel. Ideally, the estimatesfor separate bits are statistically independent. This ideal may beviolated in practice. A received word is comprised of a collection ofreceived values.

FIG. 12 is a simplified block diagram illustrating a decoder, inaccordance with certain aspects of the present disclosure. FIG. 12 is asimplified schematic 1200 illustrating a portion of a RF modem 1250 thatmay be configured to receive and decode a wirelessly transmitted signalincluding a punctured encoded message. The punctured code word bits maybe treated as erased. For example, the log-likelihood ratios (LLRs) ofthe punctured nodes may be set to 0 at initialization. De-puncturing mayalso include deshortening of shortened bits. These shortened bits arenot included in a transmission and, at the receiver/decoder, shortenedbits are treated as known bits. In various examples, modem 1250receiving the signal may reside at the UE, at the BS, or at any othersuitable apparatus or means for carrying out the described functions.Antenna 1202 provides an RE signal 1220 to a receiver. RF chain 1204processes and demodulates RF signal 1220 and may provide a sequence ofsymbols 1222 to demapper 1226, which produces a bitstream 1224representative of the encoded message.

Demapper 1206 may provide a depunctured bitstream 1224. In one example,demapper 1206 may include a depuncturing module that can be configuredto insert null values at locations in the bitstream at which puncturedbits were deleted by the transmitter. The depuncturing module may beused when the puncture pattern 1210 used to produce the puncturedbitstream at the transmitter is known. Puncture pattern 1210 can be usedto identify LLRs 1228 that may be ignored during decoding of bitstream1224 by convolutional decoder 1208. The LLRs may be associated with aset of depunctured bit locations in the bitstream 1224. Accordingly,decoder 1208 may produce decoded message 1226 with reduced processingoverhead by ignoring the identified LLRs 1228. The LDPC decoder mayinclude a plurality of processing elements to perform the parity checkor variable node operations in parallel. For example, when processing acode word with lifting size Z, the LDPC decoder may utilize a number (Z)of processing elements to perform parity check operations on all edgesof a lifted graph, concurrently.

Processing efficiency of decoder 1208 may be improved by configuringdecoder 1208 to ignore LLRs 1228 that correspond to punctured bits in amessage transmitted in a punctured bitstream 1222. The puncturedbitstream 1222 may have been punctured according to a puncturing schemethat defines certain bits to be removed from an encoded message. In oneexample, certain parity or other error-correction bits may be removed. Apuncturing pattern may be expressed in a puncturing matrix or table thatidentifies the location of bits to be punctured in each message. Apuncturing scheme may be selected to reduce processing overhead used todecode the message 1226 while maintaining compliance with data rates onthe communication channel and/or with transmission power limitations setby the network. A resultant punctured bitstream typically exhibits theerror-correcting characteristics of a high rate error-correction code,but with less redundancy. Accordingly, puncturing may be effectivelyemployed to reduce processing overhead at the decoder 1208 in thereceiver when channel conditions produce a relatively high signal tonoise ratio (SNR).

At the receiver, the same decoder used for decoding non-puncturedbitstreams can typically be used for decoding punctured bitstreams,regardless of how many bits have been punctured. In conventionalreceivers, the LLR information is typically de-punctured before decodingis attempted by filling LLRs for punctured states or positions(de-punctured LLRs) with 0's. The decoder may disregard de-puncturedLLRs that effectively carry no information based, at least in part, onwhich bits are punctured. The decoder may treat shortened bits as knownbits (e.g., set to 0).

Example: Compactly Described Lifted Ldpc Code Features

Certain systems (e.g., 802.11n, 802.11ad, WiMAX, ATSC, etc.) may use amulti-edge (ME) type low-density parity-check (LDPC) code structure.Multi-edge type LDPC codes may have advantages over the standardirregular LDPC codes. The ME framework may provide a framework fordesign of high-performance LDPC codes by using state nodes. Themulti-edge type LDPC code structure may provide many more degrees offreedom than the standard irregular LDPC codes, which can be exploitedto design codes with excellent performance, low encoding/decodingcomplexity, and/or other desirable properties. ME codes may have anaccumulate chain of degree 2 parity-bits which make the code systematicand, thus, easy to encode.

ME type LDPC codes may appear in the form of protograph based LDPCcodes, in which the ME type LDPC codes are formed from a baseparity-check matrix (PCM). As described above, the protograph and PCMsare used to represent an (n,k) LDPC codes. The PCM defines the basestructure or the edge-types in the code.

As described above, LDPC codes can be lifted by taking Z (size of thelift) copies of the base PCM and assigning random permutations(according to integer lifting values k) to each edge bundle tointerconnect the Z copies and obtain the final PCM. The final PCM has ablocklength Z times the size of the base PCM. Typically, the permutationused is a cyclic permutation (e.g., using circulant matrices to obtainthe final PCM). The final PCM can be represented by replacing thenon-zero entries in the base PCM by integers up to the size Z−1. Theinteger represents the cyclic shift (by that integer value) associatedto the lifted bundle of edges in the lifted code structure.

In some cases, a range of blocklengths may be transmitted. In this case,different values of Z can be used for the same base graph to achievedifferent blocklengths (since the blocklength is equal to Z times thelength of the base PCM). To obtain different code rates, different PCMsand/or different permutation (lifting values) can be used, for example,for a same lifting size Z.

As an example, in the 802.11n standard the base PCM has codeblock lengthequal to 24 and the lifting sizes are given by Z=27, 54, 81. This givescodeblock lengths of 648, 1296 and 1944, respectively (e.g., bymultiplying 24*27, 24*54, and 24*81, respectively). In the example ofthe 802.11n standard approach, a unique PCM is defined for each coderate and each blocklength. In 802.11n, there are four code rate points,thus, the number of defined PCMs is twelve (e.g., one PCM for eachcombination of the 4 code rates×3 codeblock lengths).

In this case, when the number of blocklengths and code rate is large(e.g., as typically is the case in long term evolution (LTE)),describing (e.g., defining/generating/determining/storing) a differentPCM for each pair of code rate and blocklength can lead to a largemicrocode to describe the PCMs (e.g., a large number of bits needed tostore the different PCMs).

Accordingly, techniques for a compact description of PCMs for largenumbers of blocklengths and code rates, while maintaining highperformance, are desirable.

A technique for generating lifted LDPC codes (e.g., lifted ME LDPCcodes) is provided herein, which lends itself to a compact descriptionand provides finely granular blocklength scaling.

FIG. 13 illustrates example operations 1300 for wireless communication,in accordance with certain aspects of the present disclosure. Operations1300 may be performed, for example, by a transmitting device (e.g., UE120 or BS 110). Operations 1300 begin, at 1302, by selecting a liftingsize value Z (e.g., leader) and a first set of lifting values forgenerating a first lifted LDPC code (e.g., a multi-edge LDPC code). Thelifting size value may be selected to achieve a target blocklength orrange of blocklengths. At 1304, the transmitting device generates thefirst lifted LDPC code by applying the first set of lifting values tointerconnect edges in Z copies of a base PCM having a first number ofbase variable nodes and a second number of base check nodes to obtain afirst lifted PCM corresponding to the first lifted LDPC code (an edge isa connection between a variable node and a check node). At 1306, thetransmitting device determines a second set of lifting values forgenerating a second lifted PCM corresponding to a second lifted LDPCcode for a second lifting size value based on the first lifted PCM andthe first set of lifting values. At 1308, the transmitting deviceencodes a set of information bits based on at least one of: the firstlifted LDPC code or the second lifted LDPC code to produce a code word.At 1310, the transmitting device transmits the code word via a wirelessmedium.

According to certain aspects, the matrix for the different lifting sizevalue in the group is generated based on the base matrix by performingan operation involving the different lifting size value and an integervalue associated with an edge in the base matrix (e.g., associated witha permutation of an entry in the base matrix), such as a modulooperations or a floor operation.

According to certain aspects, a plurality of lifting size values (e.g.,leaders) can be selected (e.g., families of a same code rate). A PCM canbe generated for each of the selected lifting size values and members inthe associated groups (e.g., families or equivalent classes) can begenerated based on the PCM for their respective leader. In aspects, thetransmitting device can store only the generated matrices (e.g., PCMs)that are based on the maximum lifting values (from which the PCMs forthe other members in the family can be generated).

Lifted LDPC codes can be described by assigning to each edge of the PCMa number (e.g., an integer) which may be less than the size of thelifting Z. That entry can be replaced with a circulant matrix obtainedby cyclically shifting (e.g., to the right), the identity matrix of sizeZ×Z, by that number. Thus, PCMs can be given by a matrix of the size ofthe base PCM with integer entries corresponding to the cyclic liftings.

According to certain aspects, a set of lifts can be defined as {a₁, a₂,. . . , a_(k)}×2^(j), 0≤i≤m, where k is number of families or equivalentclasses (e.g., associated with a same code rate), a_(j) is family leader(e.g., a positive integer), and m is a maximum power of 2 (e.g., thenumber of members in each family or granularity of blocklengths that canbe obtained). The smallest power of 2 may be 0, and the largest power of2, m, may be a large number (e.g., 10) depending on the maximum desiredblocklength.

Each family j∈[1:k] can be described (e.g., generated) by its leader asand its power of 2 up to the maximum power m. In this case, there are(m+1)k lifting values. As an example, for four families or equivalentclasses (k=4), a maximum power of 2 of six (m=6) can be used, where theleaders of the four families can be 16 (a₁=16), 20 (a₂=20), 24 (a₃=24),and 28 (a₄=28). In this the example, the lifting values of the fourfamilies can be defined (e.g., generated) based on power of 2 of theleader up to maximum power m (6 in this example). Thus, the possiblevalues of the lifts for the four families in this example can be givenas:

Z = 16 × {1, 2, 2², 2³, 2⁴, 2⁵, 2⁶} Z = 20 × {1, 2, 2², 2³, 2⁴, 2⁵, 2⁶}Z = 24 × {1, 2, 2², 2³, 2⁴, 2⁵, 2⁶} Z = 28 × {1, 2, 2², 2³, 2⁴, 2⁵, 2⁶}

corresponding, respectively, to:

Z = 16, 32, 64  128, 256, 512, 1024 Z = 20, 40  80, 160, 320, 640, 1280Z = 24, 48, 96, 192, 384, 768, 1536 Z = 28, 56, 112, 224, 448, 896, 1792

If independent lift values are used for each lift (e.g., blocklength),then (m+1)k PCMs (e.g., one PCM for each lifting value) are defined foreach code rate point. In the example described above, for the fourfamilies and maximum power of 6, 28 PCMs (e.g., (6+1)×4=28) are defined.

According to certain aspects, instead of defining (e.g.,obtaining/generating/determining/storing) a PCM for each lifting value,a single PCM can be used for each family, for example, only the PCMcorresponding to the largest lifting in the family (e.g., the leadertimes the maximum power of 2). For a family j, the PCM can be generatedfor the largest lifting value a_(j)2^(m). The other lifting size valuesin the family include the leader multiplied by the other powers of 2.PCMs for the other members of the family can be obtained based on thePCM for the largest lifting. For example, edges in the PCM for theleader can be associated with a set of lifting values. PCM for the othermembers in the family of codes can be obtained by performing anoperation involving the PCM for the largest lifting size value (e.g.,based on the lifting values) and the desired lift size (e.g., the liftsize of that family member). The operations may include a modulo withrespect to the desired lift size, a floor operation, or other operation.For example, if an edge has a value s (e.g., an integer value) in thePCM (e.g., for the largest lifting size value) of the family j, then thecorresponding integer value in the PCM for the desired lifting sizevalue l, l<m, can be given by s mod a_(j)2^(l). In the example of thefloor operation, the corresponding integer value may be found by/floor(s*(desired lifting size value)/(maximum lifting size value)):

${{floor}(x)} = \left\lfloor {s*\frac{l}{\max\mspace{14mu}{lift}}} \right\rfloor$

For each code rate, a PCM can be described for each family whichcorresponds to the PCM of the largest lift size in that family. Thus,for each code rate point, there are as many PCMs as there are families.

In the example described above, for each code rate, four PCMs may beused—one PCM for each of the maximum lifting size value of the fourfamilies 1024, 1280, 1536, and 1792, respectively. That is, the PCMdescribed for each family is for the largest lift size. In the case ofthe family with the leader of 16, an edge in the base graph (e.g., thePCM for the largest lifting size value in the family of 16 is16*2{circumflex over ( )}6=1024) may be associated with an integerlifting value s of 678 (“s” is the value of the integer which representsthe cyclic lift for that particular edge.) Values associated to alledges in the base PCM may be less than the maximum lifting size (1024 inthis example). To obtain the integer value corresponding to the sameedge in the graph for a different lifting size in the family, theoperation s mod Z (e.g., when Z=128 the operation is 678 mod 128=38) canbe performed to generate the lifting values for the PCM for that memberof the family. Thus, when lifting with the lifting size value Z=128, forthat edge, a circulant matrix of size 128×128 may be used, for example,which is the identity matrix (of size 128×128) shifted to the right by38. Although in this example, a modulo operation is used, in otherembodiments, as discussed above, a different operation may be used(e.g., a floor operation or other operation).

LDPC codes are often designed so that the decoding graph has few smallloops, for example, due to the nature of the iterative decoders whoseperformance degrades in the presence of small loops. A loop (or cycle)is defined as a closed path with no repeated nodes. This implies it hasan even length. Liftings can be chosen to achieve loop properties in thegraph. Accordingly, it is desirable to have a scheme for generating LDPCcodes for multiple liftings that all have good loop properties (e.g.,few, or no, small loops). Decoding LDPC codes to find the most likelyoriginal message involves passing probability messages around the graphof an LDCP code. The decoding is usually quickly computed if the graphcontains no loops. Unfortunately, strong LDPCs use loops in theirgraphs. As a result, the LDCP algorithm is iterated repeatedly until itis told to stop or it converges to a solution. The reason is that in ashort loop the value of an incorrect bit will propagate back around toitself, effectively reinforcing its belief and resisting efforts of theLDCP algorithm to correct it. However, this effect is diluted withlonger loops, and does not affect the decoder's performance as much.

Taking the modulo with respect to any arbitrary lift size (e.g., a liftsize that does not belong to the family) could lead to generating a PCMthat has bad loops/sets, which can lead to error-floors and degradationin performance.

Each family j may be designed (e.g., optimized) such that taking themodulo within a family does not cause, or minimizes, the formation ofbad loops. For example, the PCM for the lift size aj can be selected(e.g., designed) such that the formation of bad loops is minimized oravoided. The lift of size a_(j)2 can be obtained by considering the PCMobtained in the first step and then further lifted by 2 so that thenumber of bad loops in the second step are minimized. This continuesuntil the PCM for the largest lift size in the family is generated.Thus, generating a family involves describing the PCM corresponding tothe largest lift size in the family by multiplying its leader and itspower of 2 up to a maximum number. Next, the lifting values for theremaining liftings in the family are obtained using a modulo operation.

According to certain aspects, for each code rate point, the PCM may beextended for an incremental redundancy (IR) hybrid automatic repeatrequest (HARQ) scheme. For each code rate point (e.g., the firsttransmission), the extended (IR HARQ) PCM can be described (e.g.,generated) for each family corresponding to the largest lift size.

Example: Independent Clustering Scheme for Efficiently Lifting LDPCCodes

In a wireless communication system (e.g., wireless communications system100), a set of error correcting codes (e.g., LDPC codes) may be used,for example, for various ranges of blocklengths and/or code rates to beused. To increase efficiency in terms of implementation and compactnessof description, it is desirable that the set of codes are related.

As described above with respect to FIG. 9, a base graph or parity checkmatrix (PCM) (having K information bits-columns and N total transmittedbit-columns) can be copied, and random permutations to each edge bundleto interconnect the copies, to provide a lifted LDPC code. Practicalcodes use cyclic permutations or circulant permutation matrices tointerconnect the copies of the lifted base graph, resulting inquasi-cyclic codes, which may be easier to implement in hardware. In anexample, for a lifting value Z, each edge in the base PCM is associatedwith an integer lifting value k in the range [0, Z−1]. The associatedinteger represents the cyclic shift of the identity matrix by thatinteger. A table may be used for the base PCM showing entries for thebit columns and check nodes. Each entry corresponds to the circulantmatrix that is the identity matrix cyclically shifted by the integervalue associated with an edge between a variable node and a check node.The entry ‘.’ May be used when there is no edge present between a basevariable node and a base check node.

When the base graph is reused without alteration the code rate (given byK/N) is same for all liftings Z (corresponding to the number of liftingsor copies of the base graph). Using different lifting values can providea set of codes (e.g., a code family) to achieve a range of block lengths(given by KZ). Thus, using different lifting values for the unalteredbase graph can achieve a set of codes with a similar code rate but fordifferent block lengths. For different codes rates, different basegraphs may be used.

To generate/describe a set of codes (e.g., code family) for a range ofcode rates and/or block lengths, one way to design the code family is todesign a different base PCM for each code rate and each lift value. Forexample, in 802.11n there are four code rates (1/2, 2/3, 3/4 5/6) andthree blocklengths (648, 1296, 1944) corresponding to the lift values of(27, 54, 81). There is a unique base PCM of size 24 bit-columns for each“tuple” (i.e., each pair of code rate and lift value) resulting intwelve base PCMs (e.g., for the combinations of code rate and liftvalue: (1/2, 27), (1/2, 54), (1/2, 81), . . . (5/6, 81)). Thus, forlarge Z, the set of liftings Z and lifting values k can lead to a largedescription complexity.

Techniques for efficiently describing/generating the set of liftings aredesirable. A set of liftings for a single parity matrix may beefficiently described as an increasing series of liftings that areclosely spaced to each other in value. This allows liftings to bespecified in a narrow range with a common set of bits, allowing for acompact description and good performance.

In an example, a transmitter/encoder device (e.g., such as a BS 110 or aUE 120) determines a base matrix that is associated with a cluster oflifting size values. The transmitting device selects a lifting sizevalue, Z, for generating a lifted LDPC code by permutations of edges inthe base matrix. The lifting size values in the cluster of lifting sizevalues are within a defined range of each other. The transmitting devicegenerates a lifted matrix based on the base matrix and/or the selectedlifting size value. The transmitting device uses the generated liftedmatrix to generate the lifted LDPC code, encodes a set of informationbits based on the lifted LDPC code to produce a code word, and transmitsthe code word over a wireless medium.

According to aspects of the present disclosure, a set liftings Z for asingle base graph or PCM, to obtain a family of LDPC codes can bedescribed (e.g., determined/generated) using lifting values that areclose to each other in value for a compact description.

The family of LDPC codes can be obtained using a base graph togetherwith an increasing series of liftings with lifting values Z₁, Z₂, . . ., Z_(n) which may be referred to herein as a “tower” of liftings. Acluster includes members which are within a defined range of each other.For example, members of a cluster may be within a certain ratio of eachother. In some cases, the values of the members of the cluster may bewithin a ratio of two of each other.

One example of a cluster is the set of lifting values {4, 5, 6, 7}having a maximum ratio of 7/4. A tower can be obtained by applying anexponential power to an integer, such as a power of 2. Thus, a tower ofclustered liftings may consist of the integers 2^(j){4, 5, 6, 7} forj=1, . . . , 7. This gives an approximately exponentially spaced set of28 values for Z. Put another way, this gives the tower Z₁, Z₂, . . . ,Z₂₈=8 (2¹*4), 10, 12, 14, . . . , 896 (2⁷*7). For a fixed j the fourlifting values are within a factor of 7/4 of each other and may form acluster of lifting values. For j=1, . . . , 7, a tower of clusteredliftings may be represented as 2^(j) {4,5,6,7}. While the presentexample includes a set of lifts within a factor of 2 as clustered, otherfactors, (e.g., 3, 4 . . . , etc.) may be used. These factors need notbe consecutive, but should be numerically within a defined range of eachother.

According to certain aspects, for any lifting size Z in the set ofclustered liftings, the associated integer lifting values k for the edgepermutations may be used for any of the other liftings in the set ofclustered liftings. For example, lifting values may be designed forZ=2^(j)4 that are also good for 2^(j) {5, 6, 7}. Thus, describing (e.g.,determining/generating/indicating/storing) a family of LDPC codes may beperformed by identifying sets of clustered lift values (associated toedges in a base graph) that are close to each other, such as within afactor (e.g., a factor 2 or 3) of each other. In the example above, thiscorresponds to identifying the set of lifting values {4, 5, 6, 7} andthe other sets in the tower of liftings, {16, 20, 24, 28}, {32, 40, 48,56}, . . . {512, 640, 768, 896}, which are within a factor of 2 of eachother. For each clustered set of liftings, the base PCM for the smallestlift value in the cluster (e.g., Z=8) may be optimized. That optimizedbase PCM may be used for the other lift values in that cluster (e.g.,Z=10, Z=12, 14). Similarly, the optimized base PCM can be determined forthe other sets of clustered liftings.

Thus, liftings within a defined range of each can be specified (e.g.,stored/indicated) other with a common set of bits. For example, j+2 bitsper lifting value may be used to specify all lifts for the four statedliftings in the cluster 2^(j) {4,5,6,7}.

These liftings may be further improved by having additional bits. Forexample, using j+3 bit to represent the lifting values k on an edge anddefining the lifting by taking the j+3 bit value modulo Z for Z in 2^(j){4, 5,6, 7} results in a lifting for Z=2^(j)*4 given by the j+2 lowerorder bits and the higher order bit affects only the other 3 liftings.Higher order bits can similarly be used. The example presents a range ofliftings within a factor of 2 of each other and all are specified usinga j+2 (or slightly larger) bits. However, other factors may be used, solong as the factors are numerically within a defined range of eachother.

Generally, optimization of lifts and graphs targets reducing the numberof small loops in the Tanner graph of the LDPC code. A loop in thelifted Tanner graph corresponds with a loop in the base graph byprojecting the loop onto the base graph. Additional optimizations maytake into account the degrees of nodes in the loops In the case ofmatched lifted graphs (e.g., cyclically lifted graphs) a loop in thebase graph is also a loop in the lifted Tanner graph precisely when thelifting values traversed in the loop reduce to the identity permutation.

According to certain aspects, using j+3 bit to represent the lifting anddefining the lifting by taking the j+3 bit value modulo Z for Z in 2^(j){4,5,6,7} results in a lifting for Z=2^(j) 4 given by the j+2 lowerorder bits and the higher order bit affects only the other 3 liftings.

For the optimization of the base graph for a set of clustered liftings,liftings values may be selected within a range [0,(2^(j)*4)−1]. In otherwords, the lifting values may be selected from a range that is smallerthan the smallest lifting size in the set of clustered liftings. Thus,in example described herein, for the tower of clustered liftings forj=1, the lifting size values may be selected from the range [0:7].

For cyclically lifted graphs, each edge in the base graph has anassociated integer as a lifting value. The value is taken positivelywhen the edge is traversed in the variable-to-check direction andnegatively in the check-to-variable direction. Given a loop in the basegraph and a lifting size Z, the base loop will also be a lifted loop ifthe loop sum of the corresponding integers is 0 or has Z as a factor.Thus, when choosing integer value in the range [0,2^(j)4] for thelifting values, the goal for Z=2^(j)4 is to avoid summing to 0 or tohaving a factor of 2^(j)4 in the loop sum. For small loops, the sumgenerally will not be large, so in general, there are more such loopswith a sum of magnitude 2^(j)4 than those with a sum of magnitude2*2^(j)4 or 3*2^(j)4. Similarly, on average, sums of magnitude 2^(j){5,6, 7} and its multiples are less frequent. Thus, the small loopavoidance design problem is similar for these closely related values,where lift values in the range [0:2^(j) 4] uses more than half the rangeavailable for Z=2^(j){5, 6, 7}. For a much larger Z, the used portionwould be smaller and there may be a bigger gap between the bestperformance available for the large Z and that achievable by restrictingliftings to a smaller Z. Thus, applying this approach over a relativelysmall range of Z values (e.g., within a factor of 2) is prudent. Hence,it is possible to find lift values that give good performance for fourvalues simultaneously.

By utilizing a range of liftings which are numerically within a definedrange along with an independent set of bits for each j with j=1, . . . ,7 the number of bits required is 3+4+5+6+7+8+9=42 bits per edge tospecify all of the liftings. By creating dependencies between differentvalues of j this requirement may be further reduced. Additionally, oftena structured LDPC graph will have special edges whose lifting values maybe determined directly. For example, the edges connecting degree onevariable nodes may always have lifting value 0. Edges on accumulatechains in encoding structures are also often set to 0. Such fixedlifting structure may not vary as the liftings vary and may be referredto as having a special invariant structure. The lifting values for suchedges can be more compactly represented. However, the number of edgeshaving such a special invariant structure is a small portion of thetotal number of edges in the graph and does not significantly detractfrom the benefits of the above method for those edges that do not have aspecial invariant structure.

Example: Nested Scheme for Efficiently Lifting LDPC Codes

As described above, liftings in a clustered set of liftings (e.g., a“tower” of liftings”) can use the same lifting values (integersassociated with the edge permutations) and, thus, the number of bitsused to specify all of the liftings and lifting values may be reduced.This size reduction may allow for a reduced amount of memory for storingdescriptions of all of the LDPC codes.

According to aspects of the present disclosure, a nested scheme forefficiently lifting LPDC codes may be used that further reduced thenumber of bits per edge in the base PCM.

As all liftings, even for different j values (e.g., liftings indifferent clustered sets), are based on the same base graph, thestructures found to work for a small j value (i.e., for liftings in thecorresponding set of clustered liftings) may be scaled and reused forlarger j values (i.e., for larger liftings in another set). For example,a structure optimized for a smaller j may be retained and scaled for alarger j in order to reuse optimized bits found for the smaller j.

In one example, a transmitter/encoder device (e.g., such as a BS 110 ora UE 120) determines a base matrix that is associated with a cluster oflifting size values. The transmitting device selects a first liftingsize value from the cluster of lifting size values for generating alifted LDPC code by permutations of edges in the base matrix. Thelifting size values in the cluster of lifting size values are within adefined range of each other. The transmitting device generates a firstlifted matrix based on the base matrix and/or selected first liftingsize value and selects a set of bits associated with the selected firstlifting size value. The transmitting device selects a selecting a secondlifting size value from the cluster of lifting size values and generatesa second lifted matrix based on the base matrix, second selected liftingsize value, and the set of bits. The transmitting device uses thegenerated second lifted matrix to generate the lifted LDPC code, encodesa set of information bits based on the lifted LDPC code to produce acode word, and transmits the code word.

In the example described above, for j=1, the set of clustered liftingsis Z={8, 10, 12, 14} may be designed using lifting values in the range[0, 1, 2, . . . 7]. According to certain aspects, the liftings valuesselected for the j=1 graph can be multiplied by 2 and used for the j=2graph, where the set of clustered liftings is Z={16,20,24,28}. In thiscase, the larger lifted graph (for j=2) inherits and improves on theloop structure of the smaller graph as the larger graph for lifting 2Zconsists of two parallel copies of the original smaller graph withlifting Z. Because the smaller graph is designed to avoid loops summingto a factor of Z, it also avoids loops summing to factors of 2Z. j=1 andj=2 are merely exemplary. In aspects, the lifting values for any set ofclustered liftings may be used for another set of larger clusteredliftings, and the lifting values can be multiplied by the factor of thedifference in the liftings sizes of the two sets of liftings.

Further optimization of the larger graph could be achieved by alteringthe lowest order bit in the liftings. For example, after multiplicationby 2 all liftings would have their lowest order bit set to 0. Moregenerally, to achieve the best possible performance, more than just thelowest order bit may be altered. For example, two or three leastsignificant bits may be altered. Generally, optimizing the three leastsignificant bits results in nearly optimal performance. This preservesthe large scale properties of the liftings (the most significant) bits,scaled up accordingly (by multiplying by 2) and then refines the details(the lower order bits) to find an optimal solution for the base graphfor the next set of clustered liftings.

In one example, the three lowest order bits may be re-optimized. For theset of clustered liftings j=1, a 3-bit optimized lift per edge may beobtained. If the lifting values for an edge in the base graph (e.g., forthe smallest lifting in the set j=1) are a, y, and z (i.e., 3 bits) inbase 2 (i.e., where each of a, y, and z is an integer values of 0 or 1),then for the base graph for the set of clustered liftings j=2, the sameedge will have lifting values of a, b, w, x, (i.e., 4 bits with one bitcopied from the j=1 family) and in the base graph for the set ofclustered liftings j=3, the edge will have lifting values a, b, c, u, v,(5 bits with 2 bits copied from the j=2 family) etc. Thus, the basegraph for the set of clustered liftings j=7, the edge will have liftingvalue a, b, c, d, e, f g, r, s (i.e., 9 bits with 7 bits copied from thej=6 family) and the bits a, b, c, d, e, f g are reused for smaller setof clustered liftings j while the bits r and s are unique to j=7. Thebase graph for the set of clustered liftings uses j common bits and 2unique bits. Thus, for all of the families j=1 . . . 7, there is a totalof seven common bits and fourteen unique bits (i.e., 2 unique bits foreach j), for a total of 21 bits to describe all seven code families.This is referred to as a “nested” scheme for describing the families ofLDPC codes. If only the two lowest order bits were re-optimized thenonly 14 bits total would be needed. In some examples, most significantbits (MSBs) or any subset of consecutive bits can be used as commonbits, rather than the LSBs. Both cases offer a substantial improvementon the 42-bit independent case.

As discussed above, certain structured LDPC graph may have a specialinvariant structure, for example, some special edges may have liftingsthat are invariant. For example, the 802.11 encoding structure, usesliftings of values 0 and 1. If this structure is retained, the structureis consistent with the above optimization of lower order bits only whenat least two of the lower order bits are optimized. This is because2x1=2; so if only the lowest order bit is optimized, the value 1 cannotbe reached as only 2 and 3 are possible values. In this case, it may bepreferable to retain the lifting value of 1. A similar technique can beused in which the low order bits are retained across different j and thehigher order bits are re-optimized. In general, some bits from a smallerj may be reused to define values for the larger j while leaving enoughbits for optimization so as to achieve good performance.

CONCLUSION

The encoding techniques described herein for high performance, flexible,and compact LDPC codes may lead to improved processor performance. Forexample, the techniques may allow for a processor to efficiently encodeinformation of various blocklengths and code rates using good codes(e.g., having few loops). For example, a device, such as a processingsystem in BS 110 or UE 120 shown in FIG. 1, may encode and/or decodecode words according to aspects of the present disclosure more quicklyor more efficiently (e.g., consuming less power) than a device encodingand/or decoding code words according to previously known aspects.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isspecified, the order and/or use of specific steps and/or actions may bemodified without departing from the scope of the claims.

As used herein, a phrase referring to “at least one of” a list of itemsrefers to any combination of those items, including single members. Asan example, “at least one of: a, b, or c” is intended to cover a, b, c,a-b, a-c, b-c, and a-b-c, as well as any combination with multiples ofthe same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a-c-c, b-b,b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c).

As used herein, the term “determining” encompasses a wide variety ofactions. For example, “determining” may include calculating, computing,processing, deriving, investigating, looking up (e.g., looking up in atable, a database or another data structure), ascertaining and the like.Also, “determining” may include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” may include resolving, selecting, choosing, establishingand the like.

In some cases, rather than actually transmitting a frame, a device mayhave an interface to output a frame for transmission. For example, aprocessor may output a frame, via a bus interface, to an RF front endfor transmission. Similarly, rather than actually receiving a frame, adevice may have an interface to obtain a frame received from anotherdevice. For example, a processor may obtain (or receive) a frame, via abus interface, from an RF front end for transmission.

The various operations of methods described above may be performed byany suitable means capable of performing the corresponding functions.The means may include various hardware and/or software component(s)and/or module(s), including, but not limited to a circuit, anapplication specific integrated circuit (ASIC), or processor. Generally,where there are operations illustrated in figures, those operations mayhave corresponding counterpart means-plus-function components withsimilar numbering.

For example, means for encoding, means for determining, means forselecting, and/or means for generating may include one or moreprocessors, such as the TX MIMO processor 430, Transmit processor 420,and/or the Controller/Processor 440 of the BS 110 illustrated in FIG. 4;the TX MIMO processor 466, Transmit Processor 464, and/or theController/Processor 480 of the UE 120 illustrated in FIG. 4; and/or theencoder 1102 of the encoder 1100 illustrated in FIG. 11. Means forpuncturing may comprise a processing system, which may include one ormore of processors of FIG. 4, and/or the puncturing module 1104 of theencoder 1100 illustrated in FIG. 11. Means for transmitting comprises atransmitter, which may include the Transmit processor 420, TX MIMOprocessor 430, modulator(s) 432 a-432 t, and/or the antenna(s) 434 a-434t of the BS 110 illustrated in FIG. 4; the Transmit processor 464, TXMIMO Processor 466, modulator(s) 454 a-454 r, and/or antenna(s) 452a-452 r of the UE 120 illustrated in FIG. 4; and/or the TX chain 1108and antenna 1110 of the encoder 1100 illustrated in FIG. 11.

The various illustrative logical blocks, modules and circuits describedin connection with the present disclosure may be implemented orperformed with a general purpose processor, a digital signal processor(DSP), an application specific integrated circuit (ASIC), a fieldprogrammable gate array (FPGA) or other programmable logic device (PLD),discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general-purpose processor may be a microprocessor, but in thealternative, the processor may be any commercially available processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

If implemented in hardware, an example hardware configuration maycomprise a processing system in a wireless node. The processing systemmay be implemented with a bus architecture. The bus may include anynumber of interconnecting buses and bridges depending on the specificapplication of the processing system and the overall design constraints.The bus may link together various circuits including a processor,machine-readable media, and a bus interface. The bus interface may beused to connect a network adapter, among other things, to the processingsystem via the bus. The network adapter may be used to implement thesignal processing functions of the PHY layer. In the case of a wirelessnode (see FIG. 1), a user interface (e.g., keypad, display, mouse,joystick, etc.) may also be connected to the bus. The bus may also linkvarious other circuits such as timing sources, peripherals, voltageregulators, power management circuits, and the like, which are wellknown in the art, and therefore, will not be described any further. Theprocessor may be implemented with one or more general-purpose and/orspecial-purpose processors. Examples include microprocessors,microcontrollers, DSP processors, and other circuitry that can executesoftware. Those skilled in the art will recognize how best to implementthe described functionality for the processing system depending on theparticular application and the overall design constraints imposed on theoverall system.

If implemented in software, the functions may be stored or transmittedover as one or more instructions or code on a computer-readable medium.Software shall be construed broadly to mean instructions, data, or anycombination thereof, whether referred to as software, firmware,middleware, microcode, hardware description language, or otherwise.Computer-readable media include both computer storage media andcommunication media including any medium that facilitates transfer of acomputer program from one place to another. The processor may beresponsible for managing the bus and general processing, including theexecution of software modules stored on the machine-readable storagemedia. A computer-readable storage medium may be coupled to a processorsuch that the processor can read information from, and write informationto, the storage medium. In the alternative, the storage medium may beintegral to the processor. By way of example, the machine-readable mediamay include a transmission line, a carrier wave modulated by data,and/or a computer readable storage medium with instructions storedthereon separate from the wireless node, all of which may be accessed bythe processor through the bus interface. Alternatively, or in addition,the machine-readable media, or any portion thereof, may be integratedinto the processor, such as the case may be with cache and/or generalregister files. Examples of machine-readable storage media may include,by way of example, RAM (Random Access Memory), flash memory, ROM (ReadOnly Memory), PROM (Programmable Read-Only Memory), EPROM (ErasableProgrammable Read-Only Memory), EEPROM (Electrically ErasableProgrammable Read-Only Memory), registers, magnetic disks, opticaldisks, hard drives, or any other suitable storage medium, or anycombination thereof. The machine-readable media may be embodied in acomputer-program product.

A software module may comprise a single instruction, or manyinstructions, and may be distributed over several different codesegments, among different programs, and across multiple storage media.The computer-readable media may comprise a number of software modules.The software modules include instructions that, when executed by anapparatus such as a processor, cause the processing system to performvarious functions. The software modules may include a transmissionmodule and a receiving module. Each software module may reside in asingle storage device or be distributed across multiple storage devices.By way of example, a software module may be loaded into RAM from a harddrive when a triggering event occurs. During execution of the softwaremodule, the processor may load some of the instructions into cache toincrease access speed. One or more cache lines may then be loaded into ageneral register file for execution by the processor. When referring tothe functionality of a software module below, it will be understood thatsuch functionality is implemented by the processor when executinginstructions from that software module.

Also, any connection is properly termed a computer-readable medium. Forexample, if the software is transmitted from a website, server, or otherremote source using a coaxial cable, fiber optic cable, twisted pair,digital subscriber line (DSL), or wireless technologies such as infrared(IR), radio, and microwave, then the coaxial cable, fiber optic cable,twisted pair, DSL, or wireless technologies such as infrared, radio, andmicrowave are included in the definition of medium. Disk and disc, asused herein, include compact disc (CD), laser disc, optical disc,digital versatile disc (DVD), floppy disk, and Blu-ray® disc where disksusually reproduce data magnetically, while discs reproduce dataoptically with lasers. Thus, in some aspects computer-readable media maycomprise non-transitory computer-readable media (e.g., tangible media).In addition, for other aspects computer-readable media may comprisetransitory computer-readable media (e.g., a signal). Combinations of theabove should also be included within the scope of computer-readablemedia.

Thus, certain aspects may comprise a computer program product forperforming the operations presented herein. For example, such a computerprogram product may comprise a computer-readable medium havinginstructions stored (and/or encoded) thereon, the instructions beingexecutable by one or more processors to perform the operations describedherein.

Further, it should be appreciated that modules and/or other appropriatemeans for performing the methods and techniques described herein can bedownloaded and/or otherwise obtained by a wireless node and/or basestation as applicable. For example, such a device can be coupled to aserver to facilitate the transfer of means for performing the methodsdescribed herein. Alternatively, various methods described herein can beprovided via storage means (e.g., RAM, ROM, a physical storage mediumsuch as a compact disc (CD) or floppy disk, etc.), such that a wirelessnode and/or base station can obtain the various methods upon coupling orproviding the storage means to the device. Moreover, any other suitabletechnique for providing the methods and techniques described herein to adevice can be utilized.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the methods and apparatus described above without departingfrom the scope of the claims.

What is claimed is:
 1. A method for wireless communications, comprising:obtaining a set of information bits; generating a lifted low densityparity check (LDPC) code, the generating including: determining alifting size value from a tower of lifting size values, the tower oflifting size values comprising a product of a plurality of power of aninteger and a plurality of lifting size values; determining a set ofcyclic lifting values; and applying the set of cyclic lifting values tointerconnect edges in a number of copies of a base parity check matrix(PCM), the number of copies corresponding to the lifting size value;encoding the set of information based on the lifted LDPC code to produceone or more codewords; and transmitting the one or more codewords inaccordance with a radio technology across a wireless channel.
 2. Themethod of claim 1, wherein the plurality of lifting size valuescomprises lifting size values within a defined range of each other. 3.The method of claim 2, wherein the lifting size values within thedefined range of each other comprises lifting size values within afactor of 2 or 3 of each other.
 4. The method of claim 1, wherein thetower of lifting sizes values comprises a plurality of families oflifting size values.
 5. The method of claim 4, wherein each family oflifting sizes comprises a set of lifting size values consisting ofproducts of one power of the plurality of powers multiplied by each ofthe plurality of lifting size values.
 6. The method of claim 4, whereineach family of lifting sizes values comprises a set of lifting sizevalues consisting of products of each of the plurality of powersmultiplied by one of the plurality of lifting size values.
 7. The methodof claim 4, further comprising storing only lifted PCMs corresponding toa largest lifting size value in each of the plurality of families oflifting size values.
 8. The method of claim 4, wherein the lifting sizevalue comprises a smallest lifting size value or a largest lifting sizevalue in one of the plurality of families of lifting size values.
 9. Themethod of claim 4, further comprising: obtaining a second set ofinformation bits; selecting a second lifting size value, wherein thelifting size values is in a first family of lifting size values, andwherein the second lifting size value is selected from the first familyof lifting size value; determining a second set of cyclic lifting valuesbased on the set of cyclic lifting values; applying the second set ofcyclic lifting values to interconnect edges in a number of copies of thebase PCM or of a second base PCM to generate a second lifted LDPC code,the number of copies corresponding to the second lifting size value;encoding the second set of information bits based on the second liftedLDPC code to produce a second one or more code words; and transmittingthe second one or more code words in accordance with the radiotechnology across the wireless channel.
 10. The method of claim 9,wherein determining the second set of cyclic lifting size valuescomprises: for each cyclic lifting value in the second set of cycliclifting values, performing a modulo operation, wherein the secondlifting size value is a divisor in the modulo operation and a cycliclifting value in the set of cyclic lifting values is a dividend in themodulo operation.
 11. The method of claim 9, wherein the second liftingsize value is selected based on a target range of blocklengths of thesecond one or more code words.
 12. The method of claim 9, whereindetermining the second set of cyclic lifting values comprises: scaling,by a scaling value, each cyclic lifting value of the set of cycliclifting values to obtain a scaled set of cyclic lifting values; and foreach scaled cyclic lifting value: copying a portion of bits of thescaled cyclic lifting value; and adding one or more unique bits to thecopied portion of bits.
 13. The method of claim 12, wherein a number ofthe portion of bits is equal to a number of the plurality of powers, andwherein a number of the one or more unique bits is equal to the scalingvalue.
 14. A method for wireless communication, comprising: obtainingone or more code words comprising a set of one or more low densityparity check (LDPC) code encoded information bits; generating a liftedLDPC code, the generating including: determining a lifting size valuefrom a tower of lifting size values, the tower of lifting size valuescomprising a product of a plurality of powers of an integer and aplurality of lifting size values; determining a set of cyclic liftingvalues; and applying the set of cyclic lifting values to interconnectedges in a number of copies of a base parity check matrix (PCM), thenumber of copies corresponding to the lifting size value; and decodingthe one or more code words based on the lifted LDPC code to obtain theset of information bits.
 15. The method of claim 14, wherein theplurality of lifting size values comprises lifting size values within adefined range of each other.
 16. The method of claim 15, wherein thelifting size values within the defined range of each other compriseslifting size values within a factor of 2 or 3 of each other.
 17. Themethod of claim 14, wherein the tower of lifting sizes values comprisesa plurality of families of lifting size values.
 18. The method of claim17, wherein each family of lifting sizes comprises a set of lifting sizevalues consisting of products of one power of the plurality of powersmultiplied by each of the plurality of lifting size values.
 19. Themethod of claim 17, wherein each family of lifting sizes valuescomprises a set of lifting size values consisting of products of each ofthe plurality of powers multiplied by one of the plurality of liftingsize values.
 20. The method of claim 17, wherein the lifting size valuecomprises a smallest lifting size value or a largest lifting size valuein one of the plurality of families of lifting size values.
 21. Themethod of claim 17, further comprising storing only lifted PCMscorresponding to a largest lifting size value in each of the pluralityof families of lifting size values.
 22. The method of claim 17, furthercomprising: obtaining a second one or more code words comprising asecond set of one or more LDPC code encoded information bits; selectinga second lifting size value, wherein the lifting size values is in afirst family of lifting size values, and wherein the second lifting sizevalue is selected from the first family of lifting size value;determining a second set of cyclic lifting values based on the set ofcyclic lifting values; applying the second set of cyclic lifting valuesto interconnect edges in a number of copies of the base PCM or of asecond base PCM to generate a second lifted LDPC code, the number ofcopies corresponding to the second lifting size value; decoding thesecond one or more code words based on the second lifted LDPC code toobtain the second set of information bits.
 23. The method of claim 22,wherein determining the second set of cyclic lifting size valuescomprises: for each cyclic lifting value in the second set of cycliclifting values, performing a modulo operation, wherein the secondlifting size value is a divisor in the modulo operation and a cycliclifting value in the set of cyclic lifting values is a dividend in themodulo operation.
 24. The method of claim 22, wherein the second liftingsize value is selected based on a target range of blocklengths of thesecond one or more code words.
 25. The method of claim 22, whereindetermining the second set of cyclic lifting values comprises: scaling,by a scaling value, each cyclic lifting value of the set of cycliclifting values to obtain a scaled set of cyclic lifting values; and foreach scaled cyclic lifting value: copying a portion of bits of thescaled cyclic lifting value; and adding one or more unique bits to thecopied portion of bits.
 26. The method of claim 24, wherein a number ofthe portion of bits is equal to a number of the plurality of powers, andwherein a number of the one or more unique bits is equal to the scalingvalue.
 27. An apparatus for wireless communications, comprising: encodercircuitry configured to: obtain a set of information bits; generate alifted low density parity check (LDPC) code, the encoder circuitry beingconfigured to generate the lifted LDPC code includes the encodercircuitry being configured to: determine a lifting size value from atower of lifting size values, the tower of lifting size valuescomprising a product of a plurality of power of an integer and aplurality of lifting size values; determine a set of cyclic liftingvalues; and apply the set of cyclic lifting values to interconnect edgesin a number of copies of a base parity check matrix (PCM), the number ofcopies corresponding to the lifting size value; and encode the set ofinformation based on the lifted LDPC code to produce one or morecodewords; and transmitter circuitry configured to transmit the one ormore codewords in accordance with a radio technology across a wirelesschannel.
 27. The apparatus of claim 26, wherein the plurality of liftingsize values comprises lifting size values within a defined range of eachother.
 28. The apparatus of claim 27, wherein the lifting size valueswithin the defined range of each other comprises lifting size valueswithin a factor of 2 or 3 of each other.
 30. An apparatus for wirelesscommunication, comprising: receiver circuitry configured to obtain oneor more code words comprising a set of one or more low density paritycheck (LDPC) code encoded information bits; and decoder circuitryconfigured to: generate a lifted LDPC code, the decoder circuitry beingconfigured to generate the lifted LDPC code including the decodercircuitry being configured to: determine a lifting size value from atower of lifting size values, the tower of lifting size valuescomprising a product of a plurality of powers of an integer and aplurality of lifting size values; determine a set of cyclic liftingvalues; and apply the set of cyclic lifting values to interconnect edgesin a number of copies of a base parity check matrix (PCM), the number ofcopies corresponding to the lifting size value; and decode the one ormore code words based on the lifted LDPC code to obtain the set ofinformation bits.